I'll just
point out that, especially for a small
house, it's rarely what you really want to have the main mix be the same as a record or video or streaming mix. Sources like vocals and acoustic instruments, where a significant portion of the audio energy in the
house comes directly from the
stage and not through the PA
system, will be relatively too low in the video compared to things like recorded sound effects and electronic keyboards where all the sound in the
house comes via the PA
system. Then, too, the equalization and effects (particularly any
reverb) suitable for the
house are not likely to be ideal for recording or broadcast.
In cases like this, I usually add a postfader
aux send (or mixbus or whatever your
mixer calls it) to the matrix for the recording and use it to bump up the
level of vocals and such and get a more appropriate mix. The ideal situation, of course, is to have a completely dedicated mix--and often a dedicated person to produce said mix--for the recording, but that's presumably not
practical.
For a large
venue, where practically all the sound the audience hears is from the PA
system, it might work out a little better to use the same mix.