If you don't need slow motion, the best camcorder in your price range (in my view) is the $859 Panasonic HC-X920. Great in low light, and, as with just about any camcorder, you will be able to flip the LCD around for self-shooting. Here it is at a Kai Bo Ten No Kata in a typical indoor fluorescent lighting situation (please watch at 1080p):
For martial arts, you're definitely going to need low light. So I agree with Bill's recommendation of the X920. It also has a FHD 60 fps mode that will give you superior image quality with some slow motion ability.