He'd be a breton or a woodelf (whichever is shorter). He would use a frost enchanted imperial sword, wear the collage robes from the clothing store in Solitute, and get an enchanted golden ring. Maybe there is a sneak bonus enchantment? Too bad there isn't pure invisibility like in Oblivion.
His skills would go into stealth, lockpicking, and pickpocketing. Maybe a bit of one handed as well.
Without mods I can't have a hobbit hole, so I guess I'll have to settle for building a house and adding a kitchen and greenhouse.
What quests do you think would be good? Alduin can be a wanna be Smaug, but can you think of any other quests that would especially fit Bilbo? I'd keep him out of the thieves guild, because he isn't actually a thief.
Additionally, I'd try to avoid actually killing humanoids (like bandits and the like) as Bilbo isn't into killing. I'd try to sneak into their camp and rob them blind though. Normally maxing out stealth is somewhat op, but I think it would fit the stealth abilities of a hobbit.
If you have any thoughts or ideas, please let me know. Oh, and what light armor do you suppose would fit the bill of Mythril?