Camera Selection
What kind of camera works best for balloon and kite mapping?
Technically, any camera will work for aerial shooting, but compact cameras in the "poin-and-shoot" class are the right size & weight for balloons and kites, and are cheap. Phones with good cameras can also work.
Most cheap consumer cameras have good enough resolution, though >2 megapixels, and closer to 8-12 is best. It's best to choose a lighter camera (< 1/4 pound or 150 grams). An older, used camera is a good option, as it is possible to lose or damage cameras if something goes wrong.
Continuous Mode
You will need a camera that can do continuous shooting (or "continuous drive"), or you will have to add an external shutter trigger (see the camera trigger page).
Continuous Shooting Consumer Cameras
See if your camera is on this list of continuous drive cameras at Digital Photography Review.
For timelapse apps on smartphones, see Timelapse Apps.