Camera: Your basic p&s camera will make perfectly fine 720HD video in good light; or 1080 if they are capable. This includes the super zoom p&s, Flips, and Zi's. Super zooms are fine as well if you need or want the reach. I have an SX20 and the 720 video from that is perfectly fine in good light and fine in room light. For shooting product reviews and such for Youtube or the like, a p&s is perfectly fine. I would stress that you get something with a variable or swivel screen. Framing yourself or doing any angles is a PIA w/out it! You can live without it, but if you're shooting yourself, save yourself the cursing and constant retakes because you're head was cut off.
Editing: You can go with the free basic editors like movie maker for windows (which I didn't really like) but the consumer versions of editors such as Vegas Platinum or Adobe Premiere are going to be good enough for you to not outgrow anytime soon. For anything less than $100, Vegas Platinum is a complete STEAL for the power it packs (I haven't used Premiere but it is supposed to be good as well). Its easily worth $150 so getting it for less, even better. Prepare for the learning curve involved, but once you get even a moderate grasp on it, it will become exponentially easier to use each time.
Sound: The internal stereo microphones on p&s will be fine for you to start with, and will give you good enough sound for sure.
I'm keeping in mind that you're starting out and trying to work with a modest budget so I can tell you, don't think you need to invest massive amounts to start out. I still use my SX20 for video and have no problem pulling it out and rolling. Enjoy learning and practicing most of all!