What kinds of cages work best?

Rabbits were not designed to live on wire floors--they're hard on their feet (which have no pads on the, like cats or dogs). If you must use a cage with a wire floor, you need to provide your rabbit with a resting board or rug for her to sit on; otherwise she will spend all of her time in her litterbox. You can find cages with slatted plastic floors, which are more comfortable, or you can use a solid floor. If your rabbit has a litterbox in their chosen “bathroom” corner, there shouldn't be much of a mess to clean up.