The heart of what a spellcaster brings to any Group is their spells. They determine most of the play style and focus for a given Discipline, but also can represent a significant task to wade through and weighing the various options. The goal of this post is to analyze the spell selections in the first five Circles and give some idea of how those options may inform the emphasis of the Discipline, play style, as well the relative use of a particular spell. The reason this will only address the first five Circles is that you get to pick spells at those Circles - starting at Sixth Circle, you are on your own and it is largely in your GM's hands.
Depending on the Optional Rules used in your game, how you address picking up new spells will change. If spells can be purchased and do not cost Legend Points, there is little reason to not learn everything you can get your fingers on. If they do cost Legend Points, you may want to be more selective of what you include in your grimoire.
Air Armor: An excellent support spell for a considerable period of time. With no Threads, +3 Physical Armor for the combatants in your Group will always be a welcome addition,
Crunch Climb: There are going to be a lot of these spells; small, but useful bonuses to a specific task. They are all useful to have around. This one is for climbing and a First Circle spell that has some longevity to it.
Earth Blend: You can blend in with your surroundings (assuming you are standing on earth or stone, which is a reasonable assumption), but you cannot move. With no Threads, it can be useful for evading pursuit, but it's biggest strength is probably in setting up an ambush.
Earth Darts: While this is a poor combat spell by any stretch of the imagination (1 Thread for WIL+6/Physical damage and poor range?), it is going to be the best damage spell you get until Third Circle. I sincerely hope you didn't want to be doing direct damage as an Elementalist.
Flameweapon: 2 Threads is a lot, but +d6 damage for the (effective) duration of the combat can be a big deal. This is a strategic choice, particularly since it means three characters can have Air Armor in the same time. I wouldn't be concerned about the Strain from exploding dice; it's worth it. The setup time on this may be tricky, however.
Heat Food: Take. This. Spell. It boosts the effectiveness of Recovery Tests and you will wonder how you would have survived without it. Elementalists can commit many sins of poor decisions with spell selection, but as long as you have this spell, your Group will probably forgive you.
Plant Talk: For a First Circle spell, this has the potential to be incredibly useful. Anything that can gather information is almost always going to be a winner in the long run. There is little reason to not take this spell.
Purify Earth: This spell is more about making friends and making the world better. It is worth taking if you find it.
Purify Water: Actually more practical than Purify Earth - this can potentially solve issues with not having access to clean water. You just have to have access to the water in the first place. It may be gross, but when desperate, you can always recycle.
Resist Cold: Unless you know about it in advance and keep this in a Matrix (it has a duration only in minutes), this spell isn't going to be very practical.
Resist Fire: The same as Resist Cold.
Air Mattress: +2 to your first Recovery Test in the morning? While not quite as incredible as Heat Food, every Group is going to want this spell.
Billowing Cloak: If your Group engages in social interaction on any basis, this spell is a must have. It is probably my favorite from this Circle - it is really that good.
Boil Water: It boils water. Quickly. There are certainly uses for this, but I have no idea why this is a Second Circle spell. While it can be used in combat, it is a six round investment to get the maximum damage; five to get even something reasonable out of it.
Detect Elementalism Magic: Wizards are able to just Detect Magic and this spell rarely sees much play. Since Astral Sight is a popular (even vital) Talent Option for Elementalists, when Detect Elementalism Magic is applicable and Astral Sight is not is something of a grey to non-existent area.
Gills: Breathe underwater? Yeah, this is going to be useful at some point.
Hunter's Sense: There is going to be some quest, at some point, when you are looking for a particular creature. You are going to want this spell for that. Otherwise, it is unlikely to come up.
Ice Spear: While it has a longer range than Earth Darts, this spell is terrible.
Icy Surface: In contrast, this spell can create a nice control effect to make an escape, enact a trap, or simply pummel foes with attacks. Windlings and Archers love this spell to death.
Path Home: You will always be able to find your way back to camp, which can be useful when exploring strange (and often horrifying) new places. If you're going to the Servos and your GM is a little nasty, this may be good back-up to prevent getting too terribly lost.
Shield Willow: If there is someone in your Group with a shield, this is another good spell to have around to help them. If you have a moment to prepare, this will improve their defenses a little. Every little bit counts. It seems like it should require a wooden shield to work, but doesn't say anything.
Small Slayer: Only useful if you can get access to someone that you fully intend on assassinating in a moment of vulnerability and don't want to directly do the deed yourself.
Sterilize Object: It is like the Purify Earth and Water spells from First Circle, but for objects. Overall, probably less useful - right up until your GM has some object you absolutely must interact with that is covered in poison. Still, not likely to come up often (or at all).
Stick Together: Awesome for "detaining persons of interest". There are likely other uses for it as well, but that is generally how it gets used. Oh, that and sticking someone to the floor and then finishing them off from range. It's not pretty, but effective.
Behind Eye: Useful if you can prepare for a fight and know that being Blindsided is going to be an issue. The 2 Threads make actually employing it once combat has begun a less tempting proposition. While there is nothing wrong here, there isn't a whole lot to recommend this niche spell.
Dispel Elementalism Magic: Similar to Detect Elemetalism Magic above, but likely to see significantly more use. Definitely a useful spell to have in your arsenal, but not the must have for this Circle.
Fingers of Wind: I like this spell. It is almost certainly going to be useful (possibly even for the most hardcore kaer-crawling Group in Parlainth) at some point. If you get the chance, pick it up. It may not be your first pick for this Circle, but it should easily make your list.
Grounding: Very specific in application - you really have to know that you will be fighting something with electricity based attacks ahead of time, or that causes a lot of Knockdown (also, this spell ends if you are Knocked Down - you have been warned). With 2 Threads, it is most useful ahead of time (it has a duration in minutes), but not so much once combat has been engaged.
Ice Mace and Chain: Here is the best damaging combat spell in the Elementalist's list. 0 Threads and WIL+5/Physical damage (which is actually pretty decent). The big selling point, however, is that a target struck is Harried unless one of the damage dice explodes. This is very good, since you either get a good damage roll, or inflict a status that the rest of your Group can take advantage of (there is no downside here).
Lightning Bolt: The implication from this spell is that metal armor doesn't protect against it, but it doesn't come right out and say that. If that is the case, this is a reasonable upgrade to Earth Darts (1 less damage, but the opportunity to ignore armor). Though I still prefer Ice Mace and Chain.
Plant Feast: Never worry about rations again as long as there is some flora alive in your area. This is worth taking, if nothing else than to remove the need for that bookkeeping ever again.
Porter: Semi-sentient humanoid piles of dirt to carry your stuff with a duration in days. This will probably be useful at some point, though this Circle has some better spells if access is an issue.
Puddle Deep: The requirement of a puddle limits the usefulness of this spell. The Effect Test is also rough until you get Willforce. This really works best when setting a trap rather than on the fly, since you can create your own puddle.
Repair: Given that the effect isn't permanent, this is useful, just not incredibly useful. It will fix broken things for a few months.
Rust: This can be a powerful debuff, though is most useful in protracted combats against few, powerful opponents with metal equipment. Which may be a somewhat uncommon setup for most some games. The Thread requirement limits how much of an impact it can have and the math will often come up with a different option working out best. Overall, Slow Metal Weapon is a better choice to reduce damage.
Sky Lattice: Without a doubt, this is a neat spell. It may never come up, or it may absolutely save your bacon. Hard to say, but you may as well if you can get access to it. Truly a utility spell.
Snuff: Neat, but nothing to write home about. It is useful to putting out fires, but with two Threads, it isn't as effective at this as you may hope.
Sunlight: Natural sunlight is created emanating from the Elementalist. Off the top of my head, I cannot think of anything in Earthdawn that is negatively impacted by sunlight.
Thrive: If you are patient, you can do some pretty impressive things with this spell. Not terribly powerful, but it can be fun and potentially earn some goodwill through your travels.
Throne of Air: If you can prepare for combat, you will probably want to cast this on yourself. It gives you a very good Avoid Blow effect and limited flight. There is a lot to like here.
Winds of Deflection: Similar to Throne of Air, though with a worse duration and one less Thread (also a slightly worse Effect Step). It doesn't cost Strain, however. With an Enhanced Matrix, this is really quite useful to have around since it can be thrown up immediately.
Air Blast: Another example of the control an Elementalist can bring to combat. This presents a difficult Knockdown Test and can grant some significant advantages to the rest of your Group if deployed before melee combat begins.
Blizzard Sphere: More an area denial spell more than an overtly offensive spell. If you can trap opponents inside, it is brutal, but with 2 Threads a little on the time consuming side. Not a bad selection, but definitely better used to deny a small piece territory on the battlefield than create an elaborate trap to deal a bunch of damage.
[Element] Spear: This is better than Earth Darts in every way, but not much better. Twice the range, one more damage. If you are still using Earth Darts, this might be worth it. When you get an Enhanced Matrix, it becomes much better, but still not a great combat spell for Fourth Circle. Also, get Air Spear. Beyond aesthetics, there is absolutely no reason to get anything else. I am inclined to treat this as one spell, not five, because there is no difference between them.
Falcon's Cloak: Somewhere between useful and dangerous is this spell. You are a bird and can cast spells, but only those that don't require speaking or moving. That may be a more limited list than you think (or a larger list than you think - where I'm going with this is I don't actually know what you're thinking).
Great Sticky Vines: If you find yourself with a need to incapacitate your foes, then this is a superb option. Possibly one of the best available.
Lighten Load: A utility spell that could be pretty useful in the right circumstances and worth picking up if the opportunity arises.
Lightning Shield: Is there a character in your Group that uses a shield? If so, do them a huge favor and get this spell. This is a great buff for anyone with a shield (especially Sky Raiders).
Lightning Step: The requirements for this spell are steep and the Weaving Difficulty is pretty high. It seems neat, but this is not going to be easy to make effective use of.
Liquid Arrow: Here is something even better than [Element] Spear for damage output with the same Threads, though you must have access to handfuls of water. That can be a thing. The Weaving Difficulty isn't a walk in the park at 10, so putting this in an Enhanced Matrix is advised not just so it can be cast every round. The water requirement may significantly cut down on the value.
Lodestone's Touch: Something of a mixed bag with insane an Insane Weaving Difficulty (13!) and 2 Threads. The range is very short as well, making the bonuses from missile weapons difficult to really take advantage of. Honestly, there isn't much here to like.
Root Trap: Similar to Great Stick Vines, though with no Threads, worse range and a worse Effect Step. It also requires a nearby tree. In all, it isn't quite as good (mostly because of the requirement of a tree nearby). No Threads can be awfully tempting at times.
Shield of Warping: This spell only works against wooden weapons, which limits it right into the realm of not terribly useful. It's so specific (though does include spears and pole-arms) that it is hard to come up with a reason to have this on hand all the time, which is really what you need your combat spells to be.
Spirits of Death's Sea: If any of your Group have an exceptional Toughness (or are willing to take Step 4 damage), this can be a good way to boost their resistance to fear effects.
Uneven Ground: The use of this spell is going to depend entirely on how your GM wants to interpret it. The Effect lists it as "enemy character", while the description says "any character". The latter reading makes more sense from the context, but... you never know. If it is the former, this is pretty amazing and well worth having. If they latter, you should just pass on it. There are better things to do with your actions.
Weapon Back: For whatever reason, this spell is one of those defining moments between an adept and their weapon. When they realize that it is more than just a tool. I like those moments a lot. It's also useful, so that's a plus.
Balloons of Mist: A utility spell that is just asking for creative uses from players. If you get access to this spell, you will probably want to select it. Though it is unlikely to be the first choice from this Circle.
Earth Staff: Neat, but unless you have a very good Melee Weapons Talent, this is ultimately useless. If you do have the investment, this may be useful for you - particularly if you fear having your gear taken away.
Fireball: By far the classic magical damage spell and easily one of the most efficient of that type for the Elementalist at 1 Thread (which means you can lob one every round with an Enhanced Matrix) for WIL+8/Physical damage with a fine range. However, the area of effect is significant and your friends may take offense, also it requires a source of fire to be present. This may be an issue. It will be pretty valuable in any conflict that has large waves of enemies engaging over time, otherwise it is going to be rather difficult to pull of successfully. While in other games it may be the gold standard, here it may not be worth your time.
Ironwood: While not incredibly useful for improving armor and weapons (it seems), it is great for impromptu fortifications. Odds are good that will be useful at some point.
Metal Scream: An effective control spell by any measure, particularly since it seems to work against only your opponents (which always makes any area effect spell better). There do have to be carrying metal objects, so this may be of dubious value against non-Namegivers. Though the effect? It makes me cringe just thinking about it. Like running a fork down sheet metal. Terrible.
Metal Wings: This spell is just bad ass. Giant metal wings that let you fly? Yes please! The duration isn't spectacular (Rank+20 minutes), but you can cast it on other people. They will thank you for that, because they will have freaking awesome metal wings to fly around on.
Nutritious Earth: This isn't likely to be a game changer (though could be very important to any Questors of Jaspree or Garlen), but it has some fun flavor and can likely earn some serious good will from Namegivers around Barsaive. I like this spell a lot, but you will probably know if it will be useful for you or not. Also, consider using it with Thrive.
Resist Poison: Always good to have up when exploring the wilderness or kaers. Additional protection against poison with a duration in hours is always welcome to an adept.
Shattering Stone: Essentially an area of effect Earth Darts, though you need to have fist-sized rocks lying around. Not bad, but there are better options to be had.
Stone Cage: Honestly? I prefer Stick Together, which seems to be more versatile and lasts longer. There may be uses for this spell that Stick Together cannot do, but I can't think of any right now (Stone Cage has a longer range).