(This belongs in the games section)
Get a paralyze spell, zap things with it and then whack them with a melee weapon. it gives you weapon experience without the risk of them pwning your face because you suck at close quarters. You want weapon levels because when you level up you can get that nice bonus to strength, which let's you carry more.
Also join the thieves guild, mages make great thieves and the guild lets you turn those ill gotten gains in to vast amounts of cash.
Join the assassins guild... because the quests are fun.
The mages guild has some really long-ass quests but you get to kill things and can get a hold of black soul gems during the course of it (let's you trap the souls of things like guards, finish the thieves guild quests first and you get something that lets you get away with killing guards).
Mages are really flexible in that they have spells that can do all the things that all the other types can, this kind of makes them stupid and unbalanced... which they are, have fun.