Many webcams come with their own recording software. I have a Logitech pro 4000 which allows a recording and I can send it via e-mail or of course use it in a Messenger setting like MSN Messenger or Skype. But, while the quality is very good for that sort of environment but I suspect it will not be good enough for your intended purpose. Webcams are relatively cheap so you may wish to experiment with one first. I would expect you to conclude that an inexpensive digital video cam will serve your purpose much better.
Yes you should be able to record to a laptop almost certainly using the bundled software with the video cam. The issue will be is your particular laptop speced up enough to do it?