[Animal]

There's a lot out there. Pick up a buyers guide for them somewhere.
I can give you some insight on my own experience.

Get as much optical zoom as possible, but stay away from digital zoom. Digital Zoom reduces picture quality.
Recharable batteries and a AC adapter are a must. Digital cameras and the use of the LCD really chews up power.
Look at some more advanced features such as being able to manually select exposure etc... You might not want them now, but in a few months you may.
I've got a 64MB compact flash in my 2.31 Mega Pixel camera and I find I get about 65 shots at max resolution, about 1MB per shot. Good memory is a must if you want decent recovery time in between pictures.
Red eye reduction ability is great, although you can fix that with a good image app. The further the flash is away from the lens, the less chance of red eye.

I guess the biggest factor in all of that is the zoom, since most camera's can't take different lenses, you're stuck with just one. I've got a 3X optical, but I wish I had 6 or more. I have 2X digital, but like I said, it reduces picture quality really badly.