user19966: I am working with a small amateur theatre group, and they would like to record their performances. We tried with a consumer-grade camcorder. positioned behind the audience, but image quality and sound quality were poor. 
For the sound quality, I guess the problem was that the camcorder's built-in microphone is not meant to record people on a stage ~10meters away, with ~100 people audience in between. 
For the image quality, well, we had some problems with the auto-focus, also the changing light conditions on stage caused trouble. e.g. sometimes the light goes off, the stage is modified in the dark and then light goes back on. In those situations, the camcorder usually tried to get a picture in the dark, which led to overexposure when the light went back on. Also, there was a situation with one actor in a spot on the left side of the stage and the rest of the stage in the dark. In this situation, the camcorder's autofocus went crazy. Apparently, it could not decide what to focus on, and tried to focus on something else every other second. 
What kind of equipment/setup do you suggest for this? 
PS: It would be a nice plus to have a live monitor, such that actors backstage can see what happens on the stage. 

user19905: Low-budget scenario:
Place camcorder on tripod. Disable auto-focus, disable auto-exposure, disable everything... Sometimes you can do it only on "PRO" cameras.
Use prime lenses with proper angle, so only stage can be seen, zoom lenses is fine too, but cheap lenses / part of matrix can make not so perfect image. Make sure, you got good focused image: create some test recordings and see in on computer, NOT on camera viewfinder.
Place mics on actors and record sound of them on any device, even on cellphones, today it very cheap. Also, you can use directed mics on scene - not so cheap, but may be better to get some "environment noises".
And spend some time on final video edit, sound mixing and so on. With minimal cost you can get good quality results.

user19491: My team of teenage volunteers does this every year for our church Christmas program. We use mostly canon vixia consumer cameras, augmented with a Sony handicam and other sources as needed and available. 
Example:  



Use sound from the house sound system as your primary source. Augment as needed or desirable with ambient. Use a clapper board so you can later sync the sound and the video.
Shoot a dress rehearsal. I like to use dress rehearsals to get shots I could never get in a live performance (dolly shots, dramatic lighting ,  then insert them into the live performance in postproduction .
Use multiple cameras from different angles. Use tripods and monopods to stabilize the cameras. 
Postproduction - get Adobe creative cloud. You lease the sections of  suite you actually use on a month to month basis. Get really good with premiere pro and audacity.
If budget permits, rent a Black magic ATEM 1 M/E flypack to . Live production is more stressful but much quicker than doing everything in postproduction. You can also use the recording from the ATEM as a rough edit template for postproduction,  rather than as the primary recording. 

EDIT:  More details as requested
We have permanently mounted vixia HFG10 and HFG30 cameras on servo PT heads, feeding a BM ATEM1 M/e with 1080P signal. You can achieve much the same (or better) effect with a good tripod and live operator for each camera.
In addition to the two fixed cameras, in this production we used additional hand held HFG10 and HFG20 cameras (2 more cameras), a Sony handicam, and an iPhone. Footage from the additional cameras was added into the recording in post production with Adobe Premiere Pro.
We used the tungsten preset white balance. Only the iPhone video was white balanced in post production.
We toggled the autofocus on to get focus quickly, then off again because the sparkles and christmas lights on stage play havoc with the autofocus.
Everything else was on automatic.
The most important part of the equation was the crew. This crew has been working together since 5th and 6th grade (5+ years now), doing live webcasts at least once per week with this equipment, and has on occasion put in 40 hour weeks for special events.

user4426: Most cameras have a mode where you can manually control all the settings.. I would set the camera to manual mode, do some tests during a rehearsal.  Adjust the exposure so that nothing is over or underexposed when the stage is normally lit, and manually set the focus such that anyone on the stage is in focus at all times.
Ideally for audio, you would use radio mics on the actors, and record the output from these, as well as a couple of ambient mics to capture the audience, but this requires a sound mixer... If the actors are being amplified already, take a feed from the sound mixer's desk into your camera.  If not, then a stereo pair of mics placed as close to the actors as possible (but not picking up feet noise) might be the next best option.
With more budget, multiple cameras, with multiple operators, long lenses, etc etc... but the points about auto exposure and auto focus would still hold true.
Monitors in the other room depend on the video output options from your camera - what model are you using?

19966: <p>I am working with a small amateur theatre group, and they would like to record their performances. We tried with a consumer-grade camcorder. positioned behind the audience, but image quality and sound quality were poor. </p>

<p>For the sound quality, I guess the problem was that the camcorder's built-in microphone is not meant to record people on a stage ~10meters away, with ~100 people audience in between. </p>

<p>For the image quality, well, we had some problems with the auto-focus, also the changing light conditions on stage caused trouble. e.g. sometimes the light goes off, the stage is modified in the dark and then light goes back on. In those situations, the camcorder usually tried to get a picture in the dark, which led to overexposure when the light went back on. Also, there was a situation with one actor in a spot on the left side of the stage and the rest of the stage in the dark. In this situation, the camcorder's autofocus went crazy. Apparently, it could not decide what to focus on, and tried to focus on something else every other second. </p>

<p>What kind of equipment/setup do you suggest for this? </p>

<p>PS: It would be a nice plus to have a live monitor, such that actors backstage can see what happens on the stage. </p>
 19905: <p>Low-budget scenario:</p>

<p>Place camcorder on tripod. Disable auto-focus, disable auto-exposure, disable everything... Sometimes you can do it only on "PRO" cameras.</p>

<p>Use prime lenses with proper angle, so only stage can be seen, zoom lenses is fine too, but cheap lenses / part of matrix can make not so perfect image. Make sure, you got good focused image: create some test recordings and see in on computer, NOT on camera viewfinder.</p>

<p>Place mics on actors and record sound of them on any device, even on cellphones, today it very cheap. Also, you can use directed mics on scene - not so cheap, but may be better to get some "environment noises".</p>

<p>And spend some time on final video edit, sound mixing and so on. With minimal cost you can get good quality results.</p>
 19491: <p>My team of teenage volunteers does this every year for our church Christmas program. We use mostly canon vixia consumer cameras, augmented with a Sony handicam and other sources as needed and available. </p>

<p>Example:  <div class="youtube-embed"><div>
                <iframe width="640px" height="395px" src="https://www.youtube.com/embed/6LQsJ650mBk?start=0"></iframe>
            </div></div></p>

<ol>
<li><p>Use sound from the house sound system as your primary source. Augment as needed or desirable with ambient. Use a clapper board so you can later sync the sound and the video.</p></li>
<li><p>Shoot a dress rehearsal. I like to use dress rehearsals to get shots I could never get in a live performance (dolly shots, dramatic lighting ,  then insert them into the live performance in postproduction .</p></li>
<li><p>Use multiple cameras from different angles. Use tripods and monopods to stabilize the cameras. </p></li>
<li><p>Postproduction - get Adobe creative cloud. You lease the sections of  suite you actually use on a month to month basis. Get really good with premiere pro and audacity.</p></li>
<li><p>If budget permits, rent a Black magic ATEM 1 M/E flypack to . Live production is more stressful but much quicker than doing everything in postproduction. You can also use the recording from the ATEM as a rough edit template for postproduction,  rather than as the primary recording. </p></li>
</ol>

<p>EDIT:  More details as requested</p>

<p>We have permanently mounted vixia HFG10 and HFG30 cameras on servo PT heads, feeding a BM ATEM1 M/e with 1080P signal. You can achieve much the same (or better) effect with a good tripod and live operator for each camera.</p>

<p>In addition to the two fixed cameras, in this production we used additional hand held HFG10 and HFG20 cameras (2 more cameras), a Sony handicam, and an iPhone. Footage from the additional cameras was added into the recording in post production with Adobe Premiere Pro.</p>

<p>We used the tungsten preset white balance. Only the iPhone video was white balanced in post production.</p>

<p>We toggled the autofocus on to get focus quickly, then off again because the sparkles and christmas lights on stage play havoc with the autofocus.</p>

<p>Everything else was on automatic.</p>

<p>The most important part of the equation was the crew. This crew has been working together since 5th and 6th grade (5+ years now), doing live webcasts at least once per week with this equipment, and has on occasion put in 40 hour weeks for special events.</p>
 4426: <p>Most cameras have a mode where you can manually control all the settings.. I would set the camera to manual mode, do some tests during a rehearsal.  Adjust the exposure so that nothing is over or underexposed when the stage is normally lit, and manually set the focus such that anyone on the stage is in focus at all times.</p>

<p>Ideally for audio, you would use radio mics on the actors, and record the output from these, as well as a couple of ambient mics to capture the audience, but this requires a sound mixer... If the actors are being amplified already, take a feed from the sound mixer's desk into your camera.  If not, then a stereo pair of mics placed as close to the actors as possible (but not picking up feet noise) might be the next best option.</p>

<p>With more budget, multiple cameras, with multiple operators, long lenses, etc etc... but the points about auto exposure and auto focus would still hold true.</p>

<p>Monitors in the other room depend on the video output options from your camera - what model are you using?</p>
