Hi there and welcome!
Yes, those little ones are sure wiggly. Here are some tips about photographing children:
http://www.digicamhelp.com/learn/people-pets/children.phpYou'll want to get a camera that has a good burst (continuous) mode, though not all work when using a flash. Make sure to get a high speed memory card.
Many of the cameras that came out this year have pretty good write times, the time from taking a photo to when you can take the next photo. I highly recommend you test it out before buying, unless the store has a generous return policy.
I have a fairly new Canon SD camera and it's pretty fast. Some digital cameras, such as those made by Panasonic, have a high speed focus mode in addition to a burst mode. As far as compact digital cameras go, they are pretty effective, particularly when shooting in good or available light.
One of the secrets of getting good shots of children is to take a lot, then discard the bad ones. Sometimes I get a good shot when I photograph a child when he or she is not aware I'm doing so.
If you take a lot of inside, low light photos, check out this thread:
http://www.digicamhelp.com/cgi-bin/yabb/YaBB.cgi?board=tips;action=display;num=1196279697
