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.
Astral Sense: This marks an awkward first entry on this list because how this spell is going to function may differ heavily from game to game. It is very similar to the Astral Sight Talent (which is an Initiate Discipline Talent for Wizards, making this even more difficult to distinguish) with some subtle differences. The primary functional differences seem to be cost (this spell has no Strain), time (once cast, the spell lasts in minutes and is a Simple action to use) and information (the spell provides significantly less, but there will also be less interference). My suggestion is to talk with your GM about the functionality of this spell. Which is incredibly helpful, I know.
Bedazzling Display of Logical Analysis: If you group engages in a great deal of social interaction, this is definitely worth looking into. There is a caveat to that, however: you must be the one doing the talking (and this specifically refers to debate). The bonus only applies to the caster, which may limit the long-term use of this spell. In the short-term, it's hard to be for it's application.
Crushing Will: Just like Astral Spear, only slightly worse in a few ways (damage and Weaving difficulties). Also, likely to be replaced by Aura Strike at Second Circle, though it doesn't have the range of Crushing Will.
Dispel Magic: Pretty much the best Dispel option available, since it is accessible at First Circle and can work on anything. It's hard to justify not having this in your toolbox.
Divine Aura: Amusingly, the name of this spell often leads people astray, since "Divine" is most commonly an adjective, not a verb. Pointless semantics that I forced you to read through aside, this is a useful spell, particularly if you are engaged in social and/or investigative games. I'm always a fan of information gathering spells, no matter how minor, because information is always powerful, but can also box your GM into a corner. When cornered, GMs can be very dangerous.
Flame Flash: Inferior range and damage compared to Crushing Will, it also affects Physical rather than Mystic Armor. This is almost always a worse option, but particularly at low Circles when meaningful Mystic Armor is a rarity (practically non-existent), compared to scorchers with a Physical Armor of 10.
Ignite: This may seem funny, but I like this spell more than Flame Flash. Ostensibly, Flame Flash can light things on fire just as well (even better!) than Ignite. However, that Thread which needs to be Woven and the slightly higher reattuning difficulty make it less useful as a utility spell when you can take advantage of a situation where something needs to be one fight right now.
Mind Dagger: What we have right here is Spirit Dart with a longer range. This is going to be the mainstay of your offensive spells until you get an Enhanced Matrix with Crushing Will in it.
Silent Converse: Unless you are involved in hardcore kaer-crawling (possibly even then), there is going to come a time when this spell is going to be useful. This is a great spell and one that should be in every Wizard's grimoire.
Triangulate: It's like a laser rangefinder. If the exact distance is incredibly important, then this could be incredibly useful. It is just too situational to give a real assessment, but it might come in useful at some point. Or might really annoy your GM who must now always give accurate distances to the yard and everyone will joke about how funny it is that distances are always in quantities divisible by five.
Wall Walker: With enough time, this can completely bypass any need for your Group to have Climbing. It's not going to be so useful in a hurry, however. Subtly different from Crunch Climb.
And His Money: If anyone in your Group has Haggle (not all Groups have this Talent), then this spell should be on your radar. It is pretty much going to make money for you. It isn't likely to be a major priority, however, since there are more interesting options.
Astral Shield: With no Threads and a decent duration, it's hard to argue against this spell. It may not come into its own at this low Circle - Spell Defense isn't a common target - but can be a winner at higher Circles when the combatants need to improve this defense that is likely to be lacking.
Clean: Pretty much exactly as advertised. It's fun, but practically that is about it.
Dodge Boost: Very similar to Astral Shield in application, just to Avoid Blow and with a slightly worse duration. It's a solid spell that is likely to see use, just not terribly sexy in function.
Rope Ladder: It can be deployed faster than Wall Walker, but doesn't necessarily provide much help to those that are utterly helpless at climbing. You probably will not need both of these spells, but if you can get it for free, it's always worth it.
Seal: There are some fun uses for this spell, and can certainly be used to provide a brief reprieve for characters in dire straits.
Vines: Probably the most useful spell at this Circle, particularly against single targets that are more threatening (getting the Harried is always a bonus).
Wake-Up Call: It falls into the same category as Clean, above.
Aura Strike: The same range as Mind Dagger, but with significantly better damage and always causes a Wound. This spell is an absolute beast and will be the go to damage spell when an Enhanced Matrix becomes available.
Catwalk: Another spell that helps with climbing. That is three for three, so far. This one also gives bonuses to resisting Knockdown. It might be good (however, the Thread requirement and duration make it of dubious value in combat), but it's hard to get excited about this spell.
Combat Fury: Remember Iron Hand? If you've been getting some mileage from that, this is very similar. It just happens to give a bonus to attack rolls instead.
False Aura: Any game that features a lot of intrigue may get some significant use from this spell. Other games may find it fun, but probably not as much. That being said, NPCs are likely to use this spell more than anyone else.
Healing Sleep: Take this spell. Take it. Take it now. You may only be able to use it once a week and have some other extremely mild restrictions on when it can be used, but every Group should jump at all of the healing they can get their hands on. This just happens to also be some very good healing.
Identify Spell: If you are getting a lot of use from Dispel Magic, this can be a solid companion to it. Not precisely the same, but it can give some insight into the capabilities of other spellcasters.
Leaps and Bounds: Everyone (effectively) gets Great Leap. It's pretty fun and can be a little awesome to throw it on all of the combatants immediately prior to an encounter.
Levitate: A classic that also has some discussion on ways it can be combined with itself to greater use. Another solid pick from this Circle.
Notice Not: Grants a bonus to sneaking tests. Useful (if someone in the Group has Silent Walk), but not exciting.
Ork Stoke: Whoever created this spell is probably an enormous jerk. However, there can be some good uses for this spell if you want to make an ork ruin everything. Political themed games will probably get the most from this.
Quicken Pace: Make your entire Group (with enough castings) move faster for a day. It's hard to argue with that.
Seeking Sight: Similar to Combat Fury, but it works with ranged attacks and you affect the target of the ranged attack, rather than the attackers. This makes it better if you have multiple ranged attacks and a single target.
Water Wings: If you have a windling in your Group, they will appreciate not having to worry about their wings getting wet again. If you don't, maybe you will meet one?
Wizard Mark: The mystical equivalent to writing your name on something. Also works against Namegivers. The actual function of this spell is suspiciously close to that of a Horror Mark and the populace at large is somewhat aware of that fact and may respond accordingly (this is to say: poorly). There are benefits to putting a Wizard Mark on each member of your Group every day, though they may not appreciate it. It would definitely be more fun if the duration was longer.
Ball of String: If you suspect that your GM may try and get you lost, it is suggested that you look into this spell. If you think that your GM would never want to get you lost in a maze or by some kind of contrivance, squint real hard and think about the person at the other end of the table. Then consider picking this spell up if it becomes available.
Binding Threads: This is a fairly powerful entrapment spell and a good way to lock someone down. The number of Threads (two) limit its usefulness in a chase scenario, however.
Buoyancy: Another spell that grants a small bonus to a specific task. This time, it's swimming. With a Thread, it's hard to cast this at a moment's notice, though the duration is in hours, which is a nice change for these spells. Decent, though nothing to be excited over.
Dust Devil: The strong indication is that this spell will affect your Group (except for you), making it of dubious use (two Threads is an awful lot for something like that). If you can convince your GM that it only affects those that you want it to, then you should probably take this spell.
Hair Frenzy: Much better than Dust Devil: no Threads and it Harries a single target. While it isn't going to be your first pick for the Circle, try and get this one eventually.
Icy Protection: With one target (you) and a limited range of use (fire effects), this isn't the most useful spell out there.
Inventory: Right here is the ability to reduce all searching and endless cataloging of a room's contents to a couple of rolls. Not going to make the "absolutely must have" list, but is going to make things easier on you out-of-character. Or at least have the fiction support how you handle things out-of-character when it comes to the loot.
Juggler's Touch: A movable area effect spell (with a manageable area!) seems incredibly enticing, right? Turns out that the math just isn't in its favor. The area effect is nice, but it can still go wrong and the range isn't so great that you can easily ruin the ranged attackers of your opponents. Really, the downside is the setup time (two Threads) and the actual effect, which is decent enough damage, but affects Physical Armor. There are better offensive spells at your disposal and much better spells for this Circle.
Kaer Knocking: Subtle and possibly the spell with the most specific use ever. Also, a spell you are going to want. It may very well not be your first pick for this Circle, but it should definitely be high on your list.
Karmic Connection: It's hard to really get the most out of this spell since it has a Thread (and also hard to justify using a precious Enhanced Matrix early on). That being said, the Karma cost isn't that high (5 points) and it can be a game changer in combat. This can bring a heavy hitter from the brink back into the swing of things in a big way.
Relax: Another solid healing ability, this increases the effectiveness of Recovery Tests and reduces the time required to use them. One more good spell for this Circle.
Repair Lock: Remember how you were totally wrecking all of those locks with Shatter Lock? This is the other half of the equation that repairs them. If you have Shatter Lock, you may consider picking this up at some point. If not, then this is of dubious use (between reattuning on the fly and the three Threads, it's hard to make use of it in a pinch.)
Thorny Retreat: So... this spell. It seems like a great idea. It can come in handy and I wouldn't be surprised if there are stories of how this spell saved someone's bacon. In general, I would consider those the exception rather than the rule. To make it work: You need to either be at peace with raw casting or have it in a Spell Matrix. This means you have to be planning a "hasty" retreat at all times. From my experience, not how most Earthdawn Groups roll. Then you need to Weave a Thread. This is cutting down on the running time. When encountered, anyone trying to get through will most likely fail the Test, but there isn't a guarantee on this one. Particularly considering how frequent the ability to spend Karma on a dexterity-only test is available. Also, the damage it does is utterly laughable; to be fair, stopping pursuit is the main goal here. End result: it's hard to make this spell work for you and there are a lot of good spells.
Trust: Right here, this is one of my favorite utility spells. The difficulty is pretty high and it is very easy to accidentally end the effect (PCs tend towards deception as a matter of course - it's just a reflection of the twisted world that is inflicted upon them). That being said, to prevent and NPC from deceiving or harming you for a few minutes? Sign me up.
Wizard's Cloak: An anti-divination effect. It's fun, but the duration isn't spectacular (minutes). The short duration makes being effectively defensive with it difficult. If you are in an intrigue heavy game, then you may be able to use this proactively to some effect.
Counterspell: If you are facing a spellcasting enemy (like, I don't know, a Horror), accept no substitutes. The raw bonus isn't spectacular (+2), but it will affect everyone in your Group, has a good duration and requires no Threads.
Giant Size: This seems much cooler than it actually is. What it comes out to be is a good bonus to strength and toughness-only Tests with a pretty short duration and limitations on the area you can use it in (there has to be enough room to fit the no longer fun-sized character).
Heat Metal Armor: Even with the two Threads this spell requires, it is exceptionally brutal to use against very tough opponents that are wearing metal armor (yet another reason to wear crystal). The range is dangerously short, but it is a damage-over-time that bypasses armor. Brutal.
Invigorate: Another good spell that improves Recovery Tests. They're high enough Circle (starting at Third) to not seriously step on the Elementalist's toes, but the sheer number of them is somewhat boggling.
Kaer Pictographs: The next level of Kaer Knocking, and it works even better in conjunction with Kaer Knocking. Once you have their attention, you can start to communicate with them through a magical etch-a-sketch.
Mage Armor: More spells to add to the "good, but uninteresting bonus" category. This one gives physical armor with one Thread and a duration in minutes. Which is quite good. In an Enhanced Matrix (because everyone has one of those lying around unspoken for) this can buff an entire Group in short order.
Makeshift Missile: I was going to do a flow chart of how to see if you should take this spell, but I realized there isn't much point. This isn't a good spell. If you have a character that uses Throwing Weapons and often runs out of things to throw, they need more help than a Fifth Circle spell with a Thread can resolve.
Mystic Shock: Very short range (4 yards) and great damage. You don't have to be able to see your target - it will go right through that wall to get the person you are eavesdropping on. Shows them talking where someone can sneak up on them! The only downside is the two Threads. This is a spell built for tagging someone through a wall, floor, or ceiling. Not a whole lot of use in combat.
Slow: A touch spell; risky. It is a powerful debuff against any opponent that relies on physical attacks and/or going quickly. The two Threads make it a relatively steep investment, so it is best saved for prolonged combats against few opponents. It's nice to have, but not a spell that is going to come up often.
Solo Flight: Yeah... you're probably going to want this. Let's just be honest. Generally, this is the first spell that Wizards take from this Circle. Don't feel bad that you aren't being an individual by taking this spell. Think of it as upholding a grand tradition of realizing that walking is for suckers.
Study Thread: Beyond reducing Strain, I'm not entirely certain what this spell is really supposed to accomplish.