Most point-and-shoots don't have remote capability, but many have built in timers and are capable of shooting anywhere from 3-15 frames automatically.

Try using SnapSort to find a camera that does what you need it to in your budget range. If you'll be holding the camera, look for one that has an image stabilizer to compensate for hand-shake. Otherwise, invest in an inexpensive tripod that will do the holding for you.

Also, read up on DPI before you make a final decision. Even low-cost point-and-shoots can produce "quality" images, however the optics (lenses) are more important than the number of megapixels.