Well, are you actually going to play the character through missions and level it up? If so, maybe you want to work on the Skill Trees of pickpocket, stealth, and speech; those skills work very well with Khajiits.
If you want it merely for the role playing; maybe you could make your character scrawny looking, very skinny and dirty-looking. Give him a wild look in his eyes. Then, as you play him, maybe only give him ragged clothes, or that outfit that only comes with the cloth pants, and make him run around barefoot and in ragged clothes. He could be a thief in order to pay for moon sugar and to get his Skooma fix, and you can hoard the stuff whenever you find it. I really wish there was a dealer so you could buy Skooma; in Oblivion, they had a Skooma dealer, as well as selling regular alcohol too I think.