I'm at work, so I can't make a full CS, but I thought I'd post a few short ideas to see what people think. These are for a (likely leaf) genin:
1) A sensor-type ninja who is naturally skilled, but overly sensitive to the point where it can be hard to "turn off" the chakra sensing.
2) A jinchuriiki who, due to losing control at one point, specializes in taijutsu to avoid a repeat of that situation. I like the idea of playing a jjnchurikii that isn't super OP, but I would understand if it isn't allowed.
3) A swordsman who either has ancestors from or his parents were immigrants from the Land of Iron (samurai place). Wants to be a great swordsman to honor his heritage/ancestors.
4) An average guy without any special abilities or powers. Kind of a "blank slate" just to see what happens. Maybe I'd give him a unique jutsu that he got by chance or something.
These are just ideas that I beainstormed - I think numbers 2 and 4 are my favorites right now, but I'm curious of your thoughts.