I don't like the idea of recording training sessions with a web-cam.

You need a camcorder. I would recommend to get a decent HD camcorder like Panasonic HDC-TM300. The latter camera is an amateur one, but it is pretty good (at least this is the one that I would like to have ) You will also need a tripod.

And you may need to think about lights. Most cameras don't record well when there is no enough light. You may also consider recording outside, but then you need to make sure that there is no too much sun.

As for software, it depends on a camera that you have. You camera may have software that will work just fine for you.

You should also consider hiring professionals for shooting a video for you and editing it.