Bob, it's actually quite easy to sync audio and video. So much so, that the video camera does not actually have to even have recording audio capability.
I recommend choosing a camera for its video qualities only. It is more important that your camera has features such as zoom, manual white balance, low light capability so you can capture the best video in all of your venues various lighting conditions from any location you set up the camera. You can record the audio straight off the PA and sync the audio and video in any video software program including MS Movie Maker.
All of the portable digital handheld recorders have a line in 1/8" stereo jack input and can record quality mp3 or 44.1 wav from the PA.
When you record direct from you mixer, it is sometimes helpful to connect a mic turned toward the audience to capture ambient room noise to include in your mix.
Last edited by Charlie Fogle; 01/10/16 04:21 AM.