I'm not normally one to advertise but check out the prices at:

http://www.internetcamerasdirect.co.uk

Make sure the camera supports removable memory, such as Compact Flash or Secure Digital. Go for a brand that has a good reputation in both Electronics/Media and Lenses, such as Fuji, Ricoh, etc (or Sony which uses Carl Zeiss lenses), some cameras are spoiled by poor lenses. It's better to go for a "Camera" name (Kodak, Olympus) than a "Electonic/Media" name (HP, Epson). If anything seems too cheap it's probably not all that good.

Make sure you have Optical Zoom (digital zoom is pointless). Make sure you have built-in flash.

If you need special drivers to connect the camera to the computer (ie it does not simply appear as a new drive when you plug it in) consider ignoring the camera software and buying a USB adaptor for the removeable memory type instead. My Ricoh needed special software and it had a horrible effect on my system. Spent under £20 on a Compact Flash adaptor, unloaded Ricoh software, and problem solved!

Get decent photo manipulation software. Many programs they supply with the cameras are not seriously up to the job. I think "The GIMP" is available for Windows, it is not easy to use, but is powerful and free. Otherwise Paint Shop Pro or Serif Photo Plus will do a good job. You will need to do stuff like resize, crop, remove red eye, so be prepared!

Most of all, have fun!