We can't see what you see
and we don't know how picky you are. We also don't know how far away the stage is from "the back of the theater".
If there is good stage lighting, then there is no "low light" issue. But manual controls - specifically iris/aperture and exposure should be set rather than use the auto controls.
Assuming we go with the "low light" you mention, the *best* you could do would be is a camera with 70mm filter diameter lens (larger is better) and an imaging chip - preferably 3CCD (or 3MOS) - 1/3" (larger is better). There is no camcorder with these specifications in your price range. The closest I can get is the Sony HDR-FX7 (the lens falls short). The Sony HDR-FX1000 meets the requirement. Both use digital tape and can connect to external memory systems if needed.
The camcorders in this "prosumer" class have lens threads that allow addition of a lens - including wide angle.
You mention nothing of audio. What is your expectation?