I film a little bit, but have not gotten overly serious about it. I, too, use the Sony/Panasonic HandyCam-type cameras and for those of us that are just wanting to do some casual filming, those kinds of cameras will work just fine. They are inexpensive, easy to carry along, and are fairly durable if you take a bit of care with them. The one real disadvantage I have found is that the view-finders on those types of cameras are pretty small, and make it often difficult to pick up the target, especially if it is very far away.
I think most of the "handycam-type" video cameras have pretty good zoom/magnification capabilities, but you want to make sure you get one that has a reasonable optical zoom. Being able to zoom in on the target in hunting/wildlife viewing situations is imperative.
Make sure you get a good, solid tripod for filming, as well. Trying to film distant objects without a tripod is difficult and frustrating,...and the results for the folks that end up looking at the video are aggravating.
Again, I am not overly serious about my filming, but if I was to have a "wish-list" of things I would want for a camera/tripod to have, this would be it:
1) camera with good low-light (lux) capabilities, a good optical zoom, "manual focus" option (this will become clear enough for you once you start trying to film), and a large, clear, color viewfinder, and remote control for camera functions, remote microphone capabilities (and remote microphone(s)
2) a solid, height-adjustable tripod with a remote control system for adjusting camera angles (not even sure if they make these, but I would assume so)
3) all of these in a small enough package to be easily carried for miles in the woods
...Of course, my wish-list would probably blow the budget number sky-high, but it is a "wish list" after all.