I would say go no bigger than you want to spend. i would have to guess that you can get a 2 GB card for at least 10 bucks some places. I wouldn't go any bigger than that unless your child is at least 6 years old. For any kid 6 years or under I would not go over a 1 GB card just because of the possibility of the card getting damaged.

of course just cave it to your computer and burn it to a disc

Because the further an object is submerged, the more pressure there will be on the components inside the camera. Apparently it cannot withstand too much pressure, like most other waterproof video cameras- unless you have something along professional lines.