Dunmers make fine mages. Good choice. (All choices are good.

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Your fire resistance will make you virtually immune to low-level Daedra's magic attacks, although you'll still have to handle their melee. That immunity will give you a good advantage if you decide to begin the Main Quest at an early level.
To elaborate on one suggestion Acadian made: After you join the mages guild, you have free access to most of the stuff lying around the guild halls; you should have no problem finding a silver dagger, which even unenchanted is a very effective weapon at low level (watch out for the "red theft marker" though; you'll get thrown out if you pick up somebody else's stuff!)
To make that dagger even more effective, use Conjuration's Bound Dagger, which briefly gives you a powerful Daedric dagger. When that spell wears off, you'll still be holding your silver dagger. And definitely don't listen to the guy who says not to use Conjuration. It's a great skill, but really should be combined with another skill to have a complete package. It works well with Illusion (summon help and then go invisible), or with Restoration (summon help and then buff the summon while it fights for you), or with Destruction (if you were to cast Weakness to Fire on that atronach, the lich's fire spell would work just fine.

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