Terfyn regarding "the bigger diameter lens will give better low light performance" - and will add that it is the combination of large lens diameter and large imaging chip (preferably 3CCD or 3CMOS system rather than a single imaging chip) that will provide the good "low-light" quality video.
The largest diameter + imaging chip cams in the consumer range from Sony, Panasonic, Canon and JVC come in around 58mm diameter for the lens and about 1/3" for the imaging sensor.
You did not tell us which Mac... Assuming it is one from the last 2-4 years, you should be OK with pretty much any of the camcorders from the above manufacturers working with the computer. Whether use of high-compression AVCHD format video is debatable. This does not usually get along very well with fast action.
Since we don't know how large the venue is, we don't know how far away "the back of the theater" is. Whichever camcorder you get, turn digital zoom off in the camcorder's options menu. Use only optical zoom if zoom is required. Audio could be an issue.
I also agree with Terfyn that the Panasonic HC-X920 should be on your short list. Large 1/2.3" 3CMOS imaging sensor array but the 49mm lens diameter is a bit small.
The JVC GZ-GX1 sports a 1/2.3" single chip COMS sensor and 46mm lens diameter - again, a bit small...
The Sony HDR-PJ710V has a 52mm lens diameter and 1/2.88 (6.3mm) single CMOS imaging chip. The price includes a built-in projector that I do not believe is worth it - I would probably stay away from this camcorder.
The Canon HF G20 is more of a "prosumer". 58mm lens diameter + 1/3" imaging chip. This should be on your short list.
Between the Panny and Canon, I'd be leaning in the Canon HF G20 direction. (I generally use Sony camcorders, but they are a bit different from those mentioned above). Be sure to include a few flash memory cards and a decent tripod (Davis & Sanford; Manfrotto - anything in the $200-$300 vicinity should suffice), an optional high capacity battery from the camcorder manufacturer and a decent case (like a Pelican 1500). And consider an external mic or two... It/they would be handy for pre/post performance/rehearsal interviews.
And assuming the video will be edited, an external hard drive for the Mac is STRONGLY suggested... in the 1+ TB size... When the video files are imported for editing, they are decompressed and transcoded so the video editor can deal with them. 60 minutes of decompressed high definition video will consume 44 gig of computer hard disc space - so starting to think about long term storage strategies now is very important.