So does that mean i can raise alchemy and sneak without leveling at all? I hope so.
Armorer is for: Not only getting a head start to reach to level 50 (when you can repair magical weapons and armor), but also to help your Endurance in the early levels, which directly affects how much new HP you will have when you level up.
Illusion is for: All the wondrous spells you will need to get into the places you need to be. Illusion is by far the most powerful magic school imo.
Mysticism: Detect Life, Soul Trap.... what's not to like? Plus, it adds to your Intelligence....
Restoration: Levels very slowly. Why not put it as a major?
Yes to the alchemy and sneaking. You will get bonuses to your Agility and Intelligence. Even as minors, these skills rocket up for me. I only use Alchemy when I need it, I do use a lot of potions and poisons, but never spam restore fatigue potions. I make what I need, and stop for a while. I sneak a lot. I can one-hit kill all my bow shots (we're talking human targets only) when I'm sneaking.
I like the Thief Birthsign. This is what I've found with Luck: cost of your spells (magicka-wise) goes down. When your magic skills are at 100, raises in Luck decrease the magicka cost of my CUSTOM spells only, not the vanilla spells in game. Since I mostly use custom spells, and those spells are devastating destruction touch ones, the lower magicka cost is wondrous for my mage, as well as for my ronin.