Back in high school, we made some 2D side-scroller for our project. Now that I think about it, it's pretty much like the Mario games, but with no platforms.
It was really simple, you were given a 'package' at the beginning of the game, and you had to deliver it to your friends house (at the end of the map). There were monsters in the way, so you'd either have to jump over them to dodge them, or jump on top of them to kill them. Once you make it to the end, you win!
I'd say go with side-scroller/platformer, OR, something with a 2D grid-movement system (like the older Pokemon games).
Short project?
I would do a side scrolling action game.
Maybe a ninja. Basic slash attack. Projectile attacks based on pick ups. Shuriken, Bow, Magics.
Allow wall jumping.
