Digicams have reached the technological level that simply setting 99% of cameras to "auto" will yield excellent, crisp shots. The following features are not equal among all cameras, therefore these are the questions you should be asking yourself:
-optical zoom: is the standard 3X enough?
-size: do you want pocket size?
-exposure time: are good night shots important to you?
-battery: do you want AA or lithium ion?
-megapixels: do you really need 10?
-LCD screen: is 3" important to you, or is 2" sufficient
-movie mode: do you want sound? what resolution suits you?
-memory: SD is best. But is it critical for you to have it?
Something to consider: flash strength is one area where there is still a large variance.Look for a strong flash.
Like I said, 99% of cameras will give you great shots. But having said that, if night shots are really important to you, you'll be upset with your purchase if realize after the fact that your camera only has a 2 second exposure time. Similarly if you wanted to take nice movies, or needed high zoom... Basically once you have figured out what's important to you, come up with maybe 5 potential cameras that meet that criteria, and honestly, all 5 will end up being excellent. Pick any of them.
For starters, head over to the Steve's Digicams webpage. That will answer essentially all your questions, and provide recommended cameras in each category.