What digital camera should I buy to film short movies?

Buy a digital camcorder. Don't worry about the photos if you only want to make short movies. Make sure it is digital if you want to do computer editing.
Before making your purchase, make sure that you go to the store to get a feel for the cameras, make sure you like the quality of the picture, and all of the features.

It depends on what you are looking to do. First off, regardless of what you would be putting, I would say a safe bet for media format would be MiniDV or DVCam. Then you need to ask yourself what you want to do with it. Are you worried about lenses and f-stops? Or do you want just a pick up and start rolling camera. You would need to look in to what would be good for you. There are many good ones out there. It's hard to name one, because I don鈥檛 know your budget or needs. Find one that suits your needs.