I'm making a character who uses heavy armour/two-handed, but they will also be proficient in only one school of magic.

Which school do you think I should choose? No Destruction.

Illusion

Restoration is always handy.

Conjuration would be the strongest. Summon atronach in one hand, bound battleaxe in the other. Add mystic binding and you're golden.

Alteration isn't too useful. You can get high powered armour with it early on though.

Restoration is more for one handed use.

Illusion is nice, but quite focused on sneaking, which you won't be doing.

Actually, destruction would be a good choice if you're doing 2-handed weapons. It gives you a ranged alternative with free damage before entering melee.

Destruction fits well with two handed. It's easy to switch from two-handed and dual casting fire balls and such. It gives you a ranged attack. Since you don't want that restoration is also an option but takes a long time to level.

I don't see illusion fitting but personally but some would disagree. You could make it work. It's either that or conjuration. Alteration is not useful for this character.