$125 Kodak Playsport: Waterproof/drop-proof/dust-proof (also available in purple or blue I think)
http://www.amazon.com/Kodak-PlaySpor...dp/B0030MITDK/
$35 X-Grip: Top handle for low shots of baby crawling
http://www.amazon.com/Opteka-Profess...dp/B003PBB4ME/
$28 16GB Memory Card with USB reader: Stores lots of videos/photos (don't buy off this link...do a search o Amazon for "16gb Transcend" and it will pop up at $28)
http://www.amazon.com/Transcend-Clas...dp/B002MY8ENW/
$20 Flexible Video Tripod: Wrap this around the grip, stick it to the fridge (magnetic feet), use it as a baby-eye-level tripod, pan/tilt smoothly
http://www.amazon.com/Gorillapod-Vid...dp/B0042FZA1S/
$20 Spare Charging Kit: eBay - two spare batteries for $10, wall/car charger for $10
About $210 total for a camera, tripod, handgrip, large memory card, and extra batteries and charger. I have one of these and it's super awesome. Turns on quick, 1-button recording, 1080p video, 5 megapixel stills. There's a newer version coming out for $179, but as far as I can tell it mainly adds a little bit better low-light (existing version already does low-light better than the other handheld cameras I've seen).
It's waterproof and sealed, so the baby can chew on it, poke it, and smash it around without damage. That's a major plus when you're around kids, especially if they are throwing food or sippy cup drinks at it. The major downside is that it doesn't have an optical zoom, but if you're mostly using it for a baby, that's probably not a real big deal since you'll be close by.
The tripod is flexible and has magnetic feet, really versatile. I love mine. The handgrip is nice because it helps to steady your hand and gives you an easy grip for following the baby around as they crawl and walk. The handle is on the top so you can get low to the ground, and you also don't have to twist your arm around if you were holding the camera itself by hand.
As far as video editing & conversion software - are you a Mac guy or a PC guy?