If no one in your group has a real knack for writing, you may run into trouble trying to make a mystery or a comedy -- writing tends to be key to the sucess of those generes. A cop/action movie might work well, and horror is usually pretty easy to conceptualize. If no one is comfortable writing dialogue, think about telling a short story with visuals only.
As WideShot said above -- if you are just starting out and trying to get some experience, take a few ideas from other movies you like, change them around, combine them, rework them, and come up with your own spin on it.