Most of the Enchantment Perks. Other than that? None.
Yep. Enchantment perks (max the first one, and the perks down the middle branch) are a must.
Alchemy is much more beneficial for all types of playthroughs than Restoration. With Alchemy, you can create health, fatigue, magicka, various poisons, etc. and you pause the game to drink them. With restoration, you have to equip, then try to cast it while an enemy attacks you and the little health you have left. The only thing I like about restoration is that you can use certain spells to heal NPC's.
lolwut? I don't even use alchemy. Why bother making potions when you can buy/find/not-even-need them? I'm lv41 now and I rarely drink potions. I usually die before I will touch one. I haven't died in about 10 hours (of gameplay) and I'm playing on Master difficulty.
Edit: Alchemy is completely useless unless you're trying to break the game with the smithing/enchanting combo.