Tough to capture ambiance of a live production with only one camera. I would suggest the following:
1. Know the show, inside and out. Know it better than the director so you can capture the most significant elements at the proper time.
2. Imagine you are sitting in the audience and the camera is your eye. Keep the focus on the action and occasionally zoom in as if you would do with your eyes if sitting in the audience.
3. Don’t forget the audio. Bad audio will negate the best video. Good audio can overcome video shortcomings, including one camera! I assume there will be a sound reinforcement system. Connect hardwired to it. Best to take an auxiliary output so there can be some adjustment to compensate for differences in live sound mixing vs recorded output. There is a significant difference. Try it during rehearsal. Record it and then critique. Be harsh on your review. Make adjustments and if necessary record another practice. Did I mention that audio is most important?
4. Record with the best camera with the best lens you can. The best camera is the best one you can get!
My $.02 worth.
Jim
Jim Brown
M & M Productions USA
Oak Ridge, TN