I'm doing an illusion and conjuration mage only right now, and it's really not so bad. Although I do not allow myself to use bound weapons, strictly atronaches and things like that.
What do I do? If I'm sticking to just conjuration, I get in sneak mode. I get in a dark corner, cast my atronach or whatever, and let them do all the dirty work. Or you can put on some armor, and summon yourself a bound bow in sneak mode and pick them off from a distance without having to get close. If you want to get close, then get the bound sword or whatever weapon.
Personally, if you don't care, I would recommend starting out as a High Elf as you automatically get an extra 50 points of magicka, plus the novice hood you find in the Helgen, starting you out at 180 magicka from the get go. I say this because some spells like the bound bow are going to be a tad costly in the beginning.
So are you not allowing yourself to use any other school of magic at all? If so, you'll need to invest in smithing/enchanting since you can't use alteration and get mage armor. In the beginning, you can try some vampire armor (they have magic enchantments for mages as well as provide armor rating). Or you can wear a robe, but wear gauntlets, boots, and helmet with a good armor rating, you will just look kind of stupid in the beginning. But I would definitely work on your armor situation if you're using bound weapons (not the bow) ASAP because you will be up close to your enemies. If you're going to be summoning and attacking from a distance, it is not as dire.
So in the beginning, I would stick to attacking from a distance, relying on a bow and summoning creatures like a flame atronach, until you figure out your armor situation and everything you want to do. Sneak will help you too. Have fun!