I got a JVC Everio disk drive camcorder 2 years ago when my daughter was born. It's small, light, easy to use and can be had for less than $250 now. 30GB HD (you run the batteries out before you use it up).
However, it gets used about once every two months. Sounds stupid or lazy, but the last thing I think about is taking the video camera after packing up diaper bag, spare clothes, snacks, juice boxes, phone, wallet, keys, etc.
Guess I'm saying...I wouldn't spend too much on one unless you're sure you'll use it.
Also, I'd look into what the video editing software is. The JVC program sucks.