Many choices here
In the typical consumer space, the last few years have been dominated by the Mini-DV digital cameras. This is digital technology but records onto small tapes. The stored image can then be transferred via "firewire" onto your PC and edited via aforementioned programs.
As also stated, more and more manufacturers are coming out with the format that lets you record right onto a small DVD.
Other important things to consider:
External microphone connector. If you ever want to make "movies", you must have the ability to use an external microphone to get close to sounds. Otherwise, you are stuck with whatever is on board.
Decent sized screen: The advantage of modern cameras is the swing out color screen that most of them have, allowing you to even frame yourself in the action by turning the screen around. However, alot of the smaller cameras have really dinky screens. Check before you buy.
Autofocus shut off: make sure you can!
Other options such as Macro, digital zoom, etc are more to your invidividual needs and tastes.
The other important feature is whether you go for a 1CCD chip or "three chip" (3CCD) camera. With a 3CCD, there is a chip for each color used, resulting in a crisper color picture and better color reproduction. Panasonic finally makes a model that is not crazily priced.
I am of the 5% or so of the video buyers out there that do not care for the consumer grade of cameras. Over the past years, they just keep getting smaller and smaller. The result, even with image stabilization, is a wavery picture with too much up and down movement. The old fashioned standard VHS camcorder that you positioned on your shoulder were actually capable of delivering a better shot with less stress. Try holding a small camera steady sometime. Better use a tripod.
And of course, working with a 3" square box is ridiculous if you want to do something interesting with it besides shooting the spouse and kids.
I purchased the Panasonic DV4020 a few years ago, and it is larger and easier to control than what is out now.
For me, Panasonic makes something perfect--a full sized, shoulder mounted but very lightweight "prosumer" model. A three CCD, semi-pro model with all the good features. You can easily spend $10K on a more professional digital camera, and this model bridges the gap. It's about $1300, so it's my next "big" purchase.
Good luck!