Mirabelle Ervine gave me some Robes of Destruction. I reckon I'll go ahead and get into the College of Winterhold quests (never done them before).
I want to use Destruction. Can someone give me a brief overview of all the other schools of magic and some spells of them? Restoration (with healing and healing hands and the wards) seems interesting... but so does Conjuration...
Also, if I use a Staff of Conjuration, will Conjuration go up?
And I'm using a Steel Mace in case I run out of Magicka.
Using staffs will not give you any experience. Your conjuration will not go up.
Alteration has Paralysis spell: it works on some very strong enemies, like Draugr Deathlords, vampires, giants, super high level mages.
Illusion has Quiet Casting perk, Invisibility, and Muffle: if you want to go stealthy.
If you invest heavily in illusion, it works on pretty much everything except dragons and dragon priests and super high level enemies.
In Destruction, people often forget about Runes, Cloaks and Walls. They are amazing and very useful.