Thanks Kam, here's the answers...
The use will be for the kid's birthdays, football games, and for getting the kids exposed to something they may enjoy, like making movies. The budget is around $600-$750 +/- based on the benefits of speding a bit more.
I haven't decided on editing software yet. There's a couple out there for around $100 which I know is not the end all, but I'm looking for basic editing, not production editing.
I can't say which video card I have off-hand, but the computer is only a few months old with a P4 3GHz processor so it should be something recent.