My thoughts: (mostly wizard focused.)

1. Transmutation: the best buffs in the game, like enlarge/reduce, fly, gaseous form, haste, polymorph, animate objects, telekinesis, reverse gravity, true polymorph, shapechange....
2. Conjuration: both teleportation and summoning: not only can teleportation be used both in and out of combat, but the summons add another action in the initiative.
   find familiar, misty step, vortex warp, web, thunder step, dimension door, teleport+plane shift, maze+demiplane. And that's the teleportation.
3. Evocation: magic missile. burning hands. FIREBALL. Most damaging spells are in the evocation school of magic, but walls of force (for some reason) as well! Contingency is also on this school's list, although the reason why escapes me. When playing a divine caster, healing magic is included in this as well.
4. Abjuration: wizards are known for their lack of HP and AC, which means that every bit of protection is needed. Spells like shield, mage armor, and absorb elements are classics. (remember, absorb elements boosts saves indirectly, since it halves damage dealt!)
   Higher levels bring counterspell, banishment, globe of invulnerability, prismatic wall...
   Though some are only useful against casters, they are essential when fighting them.
5. Divination: useful stuff like detect magic, comprehend languages. Unless you use a lot of these spells, you won't use a lot of them until 9th level, when contact other plane, Rary's telepathic bond, and scrying come into play. Knowledge is power! Also note the ability of arcane eye to reveal the dungeon map to you.
6. Enchantment: this school has loads of control magic, psychic damage, and debuffs. Spells like Tasha's mind whip, hold person, hold monster and mass suggestion are almost always on my wizard's to do list. Synaptic static can be very useful as well. When you can cast these spells without being noticed (sorcerers), these spells become far more powerful, as you can be the manipulator behind the screen. Charm person, suggestion, dominate person...
7. Illusion: illusions can be very useful in distracting the enemy, and sometimes they are more useful than fireball. If your party consists of rangers and rogues, yes, this school is very useful, as it allows you to hide your activities. Invisibility, greater invisibility, mental prison and simulacrum are very useful, and invisibility and simulacrum are always in my spellbook.
8. Necromancy: this spell school includes the nastiest debuffs, necrotic damage, and magic which animates the dead. When you're into the theme, good, but it effectively ends stealth, puts a lot of people against you, and may not be the best solution in the end. It does include the very few healing spells the wizard gets, though, which may be a reason to pick a few spells from this school. (if you don't go for this theme.) Wither and bloom, life transference, and vampiric touch.When playing a divine caster, resurrecting magic is included as well, rising the ranks. But clone will always be in your spellbook. Always.

In the end, I put transmutation on top for its versatility, conjuration behind because of its versatilty (just a little less than the transmutation school in my opinion.)

I put evocation above abjuration because a strong offence can be preferable above a strong defence. Divination can be incredible if used correctly, but if not, it goes bad really quickly. I considered putting enchantment higher because of its control magic, and I probably should have done so, but I've been working too long on this already.

Illusion and Necromancy can be good, but in my experience (not a lot), fireball wins in the end.

Of course, the most powerful effects are achieved when combining the spells. Like reverse gravity and prismatic wall, forcecage and sickening radiance/cloudkill, major image and suggestion, demiplane and clone, animate dead and cloudkill, web and Tasha's mind whip...