I have always been partial to illusion magic in Skyrim, I like that you can bend others' wills with almost no effort and when beginning a new game with a stealth build muffle is a great spell, alteration second for the purpose of strengthening spells such as Oakflesh.

I always say to myself I couldn't be a wizard, mainly because I know that if I knew how to do any magic whatsoever, I'd use it for the most menial stuff imaginable. Using alteration to turn my chicken vindaloo into a caesar salad or something.

Adventuring?

Saving the world?

Nahhh.

But most of all, if I was a wizard, I would choose conjuration because with that you could summon daedra. And while ingame dremora aren't particularly talkative (except when practing a bit of Spontaneous Evisceration) that wouldn't stop me from trying. What's their life like? Do they have dinner? What's his favourite? Has he ever thought about what it's like not being a dremora? Does he have any friends? Is he married? What's his favourite cheese and why isn't it Red Leicester? That sort of thing is why I would choose conjuration. Just to see what's going on in the other aisle.

From lore perspective, Alteration is the most interesting imo. However, I mostly use Restoration when I play the game.

I usually don't play as a mage or anything, but destruction magic will always be useful for me. By casting flames at magical barriers or killing the bears that for some reason always gets stuck in the "cielings" of caves and can't shoot arrows or hit them.

But usually when I do play as a mage my favorite destruction spells are shock ones because they're the most effective with almost every enemy.

Destruction so I can destroy my opponents

Conjuration. It's very cool to see your Daedra Lords squishing your foes.

I like of Destruction combined with Conjuration