This can get very expensive. Look for a camera with a rechargeable battery. Better yet, get one that can be recharged while it's in the camera. That way you can always carry spares. There are some weird-looking digital cameras out there.
Some designs make it easier to take pictures, others make it harder.
Some camera makers omit the traditional viewfinder altogether in favor of an LCD screen on the back of the camera. But instead of holding the camera up to your eye in the time-honored fashion, you'll have to hold it about a foot in front of your face to see what you're taking. This may not be comfortable for bifocal wearers, and it's harder to hold one of these cameras steady. Also, look for a shutter and other adjustment buttons that are easy to find. It's no fun fumbling when you should be concentrating on composing your pictures.