These class descriptions are meant for informative purposes and you can, of course, use your imagination in any way that you would like as you build and progress your character.
The wizard in DnD 5e is an incredibly overpowered character in the right hands. Even in the wrong hands a wizard can still deal obscene damage and change the world. Depending upon how lax your DM (I'm middle of the road: expect a link here in the future) is regarding the cost of learning spells and the cost of casting certain spells, this is arguably the single most powerful class (Read: Classes Ranked) in the game. Keep that in mind while deciding which Arcane Tradition to choose. Even if you choose the worst School of magic, you will still be powerful.
10: Conjuration
You can teleport without Misty Step and make summons stronger eventually. Yay?
It will likely come as no surprise to anyone to find this at the bottom of the list. This School of magic is very lackluster, even in terms of flavor. I struggle to find any value in Minor Conjuration. The only potential I see is an ability to dupe a shopkeeper or NPC into buying the item, but you would not be able to return to that shop in the future. Unless you're in a party of murder hobos.
Benign Transposition allows you to teleport yourself or switch spaces with someone. While this sounds great, you can just get Misty Step. The final skill allows you to give a summon 30 temporary hit points which is very interesting but not particularly powerful that late in the game. Also, summons will likely just annoy your DM.
9: Echantment
You're incredibly charming without all the charm and charisma. You could have been a bard if you stopped reading, nerd.
At first glance, if you do not look into it too deeply, this School seems much more powerful than it truly is. The Hypnotic Gaze sounds useful, but as you're a squishy wizard you really shouldn't be standing 5 feet away from an enemy concentrating on a spell just to keep one combatant out of the fight. The fact that you can potentially divert an attack once per day is neat, but other Schools do it better.
Split Enchantment, however, may make this worth choosing. You get to dual cast a single target enchantment spell. You also don't have to be within arm's reach of anyone to accomplish this so that's a win. Are charm spells really all that great, though? You decide. I'm not impressed. Most of all, your final skill that you gain with this School is a big let down.
8: Illusion
You make better illusions. The greatest illusion is that people are convinced this is an amazing school.
I know this will upset some hardcore Illusion lovers but I just do not see the beauty of this School. This School of magic is highly dependent upon what your DM will allow you to get away with when it comes to illusory magic. If your DM will let you distract an enemy every single turn or remove combatants entirely without them rolling saving throws then this has a much larger potential. Generally, I find this to be very disappointing compared to the general hubbub around the community. Your illusions can make sound and be illusions which is better than just one, but still not going to change the world.
You also gain the ability to change an illusion while it's active which I find to be almost entirely useless. You're a wizard. Do something better with your time and concentration. You do get to force a missed attack once per short rest which is undeniably great; however, the final skill sounds much better in theory than it truly is in practice. As an example you can create an illusory bridge that becomes real for a minute. Just cast level 1 Floating Disk as a Ritual instead. You save a spell slot and it is much more exciting.
7: Transmutation
You're an alchemist that becomes a single spell cleric in your later adventuring days. Maybe you should have been an artificer instead?
The first skill that you gain with this is virtually useless but once you get your Transmuter's Stone this becomes interesting. You gain access to a pretty unique ability to buff yourself or one party member by handing them a rock. You're a more useful penguin.
Shapechanger adds a free spell but nerfs it simultaneously; however, your top tier skill can be very powerful. Through Master Transmuter you can cast Raise Dead or even remove all curses, diseases and poisons from a party member while simultaneously healing them to full health. This makes the School worth picking just for utility.
6: Necromancy
Not just for Halloween kiddies. Who doesn't like being ghoulish?
This makes it so far on the list mostly for flavor because I love the feel of this School of magic. Beyond that, it does come with some unique skills. This starts out strong with Grim Harvest which allows you to heal yourself for two times the damage dealt when you kill something, or three times if it is a Necromancy spell. This can be quite beneficial at lower levels and still helpful later on. A fun combination is this plus Vampiric Touch. As a level 3 Necromancy spell you'll heal yourself for 9 health. Tack on the one half of 3d6 damage as well and you went from being nearly dead to being at full health.
The two mid-tier skills are lackluster. Summoning a zombie or skeleton with slightly more hp that still doesn't deal damage is pretty boring. Again, you'll just annoy your DM. Resistance to necrotic damage is thematic and cool but not particularly powerful. The crowning achievement of this School can change a battle, though, when you take control of an undead enemy regardless of challenge rating.
5: Bladesinging
A wizard that flits around melee combat and is harder to hit than its squishy counterparts. Let's dance.
This is the only School of magic that gives you additional proficiencies. You gain light armor and a one handed melee weapon which makes you more interesting immediately. Unfortunately, a shield is not included, but with high Dex you are a viable melee combatant dancing around the battlefield that slings spells left and right. In addition to proficiencies, you also gain a bonus to your AC that matches your Int modifier, increased walking speed and a bonus to concentration saving throws.
Keep in mind that throughout all of this, you are still a full wizard. Your wizardly power has not been diminished at all and you even get an extra attack in combat. Even better, you can attack then cast a cantrip on the same turn. Eventually you get to cut the damage you take in combat by expending a spell slot and you add your Int modifier to melee attacks. All in all, this has tons of roleplaying flavor and is a very fun Arcane Tradition.
4: War Magic
You are considerably more durable than your wizardly friends and you are much more likely to be first in initiative. Make war, not love.
Every additional skill that comes with this School adds something desirable. This starts out strong with two additional features off the bat. One of which can help you not get hit by a spell or physical attack and the other allows you to add your Int modifier into your initiative every time you fight. You're off to a great start and your next skill lets you add damage to a number of attacks per day equal to your Int modifier for all intents and purposes just for casting two of my favorite spells (dispel magic & counterspell). Getting even better.
Once you reach higher levels in this Arcane Tradition you gain +2 to AC and all saving throws while concentrating on a spell. You were going to be concentrating anyway, why not get a perk? The final feature of this School is a bit lackluster but it does functionally negate the worst part about the first feature.
3: Abjuration
Protect yourself and protect your friends while destroying your enemies from afar. If you die you did something very wrong.
Every time you cast an abjuration spell you get a free shield that serves as temporary hit points. This is incredibly powerful for a low level wizard as it can functionally double your hit points at level 1. It becomes less powerful as you continue your adventuring career but it remains helpful all the way to level 20. When you hit level 6 you can even extend this over your fellow adventurers instead of giving it to yourself. If you're a good wizard and you're successfully staying out of the fray, this is a solid idea.
I've already mentioned that I love Counterspell and Dispel Magic and this class boosts both of those by adding your proficiency bonus to the ability checks when you cast them. The final feature of this School is amazing. It provides you with advantage on all saving throws against spells and resistance when you do take damage from spells. Now you're just casting counterspell to be sweet to your friends because you don't need it yourself.
2: Evocation
You are pure (incredibly intelligent, yet) unthinking carnage in combat. Blow up the whole world without friendly fire.
As a wizard you can control an entire battlefield. Never forget that. With that being said, you can also blow up all of your enemies and Evocation spells are often the best way to do that. Tack on the fact that you can cast all of your area of effect spells and negate your fellow adventurers from getting hit by them and you have an absurdly powerful build out the gate. No need to convince your DM you cast fireball in the back right corner of a map and accidentally burn down the house. Just cast it in the middle of the room.
Potent Cantrip may not sound powerful at first glance but it really adds up. Half damage on a cantrip that an enemy succeeds on a saving throw takes a wasted turn and makes it successful. You then get to add your intelligence modifier to your evocation spells. You can do this unlimited times per day as written, so unless your DM nerfs this as some will, this is insane. To top it all off you get Overchannel as your final feature which allows you to deal maximum damage automatically on any damage dealing spell from level 1 – 5. This comes at a cost if you use it more than once per long rest, but it's a moderate risk for a very high reward. This would actually make more sense thematically for a Necromancer but lo and behold, they gave it to the Evocation wizard. Have fun being a firebrand.
1: Divination
You can literally change the world around you and you know it. I can see you picking this.
Allow me to be very clear: you get to start off this Arcane Tradition by changing the results of any roll twice per day based upon the results of 2 d20s you roll to start every long rest. ANY roll. The power of this ability can not be overstated. It is not quite game breaking but as a DM I find this to be world shaking almost every time my divination wizards use it. Your other low level skill gives you spell slots back when you cast a spell from the divination spell. Yes. You just cast free divination spells for all intents and purposes. Enjoy.
The first higher level ability that you get is comparably lackluster but it is highly thematic to a divination wizard and fun to play with. It provides you with darkvision, the ability to see into the ethereal plane, the ability to read any language or the ability to see invisible enemies up to a certain distance. Remember those 2 d20s that you get at a lower level, though? You now get 3 of those instead as your final feature. In my opinion you just made the single most overpowered feature of any subclass in DnD 5e 50% better. Have fun toying with your DM.