Easiest one for cycling is one you can operate easily- Small enough to go into a jersey pocket- but large enough to handle. I have a Sony Cybershot with 10.1 pixels and a large rear viewing screen. It also has an SD card that loads into the computer for ease of transferring pics. Have had several Sony cameras and I like them but other makes are probably just as good.

So any point and shoot- a Memory card that is large enough for plenty of pics or videos and a rechargeable battery. Not much else required.