[Omega]

If you will be using a tripod, you can use any semi-decent camera but go for the manual settings for more control.

If you don't have a tripod, the problem is more of the light-intake rather than the actual manufacturing. Even some of my favorite cameras can't handle performance pictures. When you're shooting at somewhere around 1/1000fs, your camera will hardly be able to take in any of the light without a flash (which is why in automatic mode, it opts to give you that brighter, non-realistic impact from artificial light) and the stage lights will not be enough to fill this need. Any $300 camera won't be able to handle these lighting conditions without a tripod or a slower shutterspeed. But if that's what you're up against, I'd suggest at least seeing about taking in a monopod (which is what sports photographers use as it gives you balance but is still very mobile) or for a really low budget, I sometimes take a bean bag with me when I want to take photos and just put in on a ledge and position your camera on that. As long as you have support, you'll be able to slow your exposure to something like 1/125 or lower which will still capture the detail and action but will let in a lot more light. If you just have to do it free-hand, hold the camera as steady as you can and bring the speed down as far as you feel comfortable with.

But if these are production photos, I assume you will have the house more or less to yourself? And then I would opt to buy a tri-, or mono-, pod. As for the camera, I might suggest the Sony Cybershot H9. You can probably get it for about $300 these days and its a wonderful, and very fast, model. Or you can get its sister model, the H7, for a little less and its the same camera without a couple features, like nightvision and a bit smaller of an LCD screen. However, the type of camera isn't all that important. I'm a firm believer in its more about knowing how to use a camera than the camera specs. So if you have a camera, play around with its settings and determine whether or not it will do the trick. If not, just buy something you think looks nice and read its manual to become familiar with its settings. Then when you get there, depending on the light, movement, and distance, you can play with its ISO, aperture, shutter speed, etc. And find something that works for you. No camera will automatically give you what you're looking for and there's no setting built to fit your performance, so I can't give you a short answer as you're just going to have to play around with what you can get.