Khajiit. A Demonhunter needs cunning, agility and a natural feline charm, no?
"Demon hunting is a very... Profitable undertaking. Rather difficult, but you will never go hungry, if you live."
Of course, choose your sideburns with care, they have a tendency to clip through hoods. Better go for the cute mustache.
Now, there is one main thing to keep in mind when choosing a Skyrim-race. It doesn't really matter to your playstyle at all after a while which race you chose, since you can close the skill-gap fairly easily. The race bonus is a suggestion, and you can do perfectly fine, even if you picked the "wrong" role. Like a Breton barbarian or a Khajiit paladin or an Orc accountant.