go to a store and actually try the camera out if it is easy to use you will usse it allot if its difficult you wont use it much.
Get 3 to 4 megpixs. 3 to 10 times optical zoom. a screen on the back. Li-ion battery(S) is a must. try to get a macro setting (for ultra closeups) get an extra mem card as big as you can afford 256, 512 meg or bigger. if you want to do movie clips make sure it has sound or you are making charlie chaplin movies. if a burst mode is available get it its a handy feature with kids (takes 2 or 3 pics at 1 sec intervals) get a pocket sized camera you will carry it and take more photos
make sure the camera will take jpeg photos cause thats what the photo labs want.
make sure the size of the pixals is in a standard size
eg 3 to 2 = 4by 6 print. (while you still get prints in a standard 4x6 or 5x7 size the corrosponding digital size doesn't always match. this means that some times the images top and bottom are cut off to fit the 4x6 print, normally not a problem but I've had some photos messed up this way
olyumpus, nikon, cannon, you cant go wrong with any of these get a sony if you want it to be a no brainer but the others do take a better photo indoors and with flash.
out side most cameras will take acceptable photos it is indoors under flash conditions that will make the difference. I recently used my sony dscs75 and my buddies cannon to take photos and the cannon did take better photos using the flash indoors
I have a sony dscs75 for 4 years and have taken 4000 photos/clips with it and its been good
my next camera will be the olympus C700 series compact digital with li-ion battery and a 512 meg card