You're going to want a camera which allows full manual control, because automatic exposure settings might come up differently from shot to shot, ruining the flow of images. And you're going to want to manually focus for the same reason. Any digital SLR or many high-end digicams will fit the bill here.

Since video is usually much lower resolution than given by still cameras, that's not much of a concern — any camera will do, and will probably have high enough technical image quality. However, the higher-quality still images you can take, the nicer your final result. For this reason, it's probably a good idea to choose a larger-sensor camera — either a digital SLR or one of the newer "mirrorless" cameras. Selecting a model with interchangeable lenses will give you more flexibility in finding a "look" that's right for your film.

If you do get a DSLR, it's probably best to get one with "live view", the feature which lets you compose on the rear LCD screen rather than the viewfinder. And, DSLR or not, a model with an articulated rear screen will make it easier to position the camera where you can both get the right shot and still see the screen, without contorting yourself into a weird position.