I wanted to start putting perks into either illusion, conjuration, restoration, or alteration. Which would you guys say is most useful?

Also, is lock picking or speech worth putting perks into?

Conjuration is awesome, and restoration is useful IMO
conjuration buffs your bound weapons, and allows you to summon more powerful allies in combat (zombies or elementals)
restoration lets you heal yourself more effectively for cheaper, so you don't have to burn through potions or worry about food
also, resto has a talent that increases magika regen by 30%, which is essential for a magic wielder

From my experience, Lockpicking isn't worth the points, and speech is fun if you vendor a lot of stuff that could be used for professions that you don't care to do.

Illusion: Buffs allies, enrages enemies, calms enemies, fears enemies, turns yourself invisible.

Conjuration: Create things out of nothing, more focused on minions (can go with bound weapons but meh)

restoration: Buff heals (works great for the paladin archtype [if you play with such a mentality])

alteration: Modify your body to negate damage mostly (less physical and magic damage)


So what do you want to focus more on is really the question you need to answer.