Take the music the musicians are producing -> amplify it as naturally as possible. That's my philosophy in a nutshell. It is called sound reinforcement; simply augment what is coming from the stage. That's what I try and instill in anyone I know who wants to mix. Sorry if it wasn't very helpful or what you're looking for.
In theater is essence you are trying to have the fact that you have a mixer and amps and speakers etc, invisible from an aural perspective to the audience. Goal is to make any position in the audience be the "perfect spot" hearing the production as the designer intended.
For theater, I think the primary goal is to make people have to question whether or not the actors are wearing mics. Along with this, the talent should be encouraged to act as if they are not wearing mics.
To combine up to dozens of inputs and route them to numerous outputs while paying attention to the needs and desires of dozens of people, not the least of whom are sitting in the audience. All the while tweaking hundreds of knobs and sliders, keeping track of dozens of cables and their routing. Not to mention loaning cables to dimwitted guitar players, tape to drummers, paper and sharpies for set lists and signs, adapters for nerds who want to record to their laptops, breaking up fights, using reverse psychology on actors and musicians, and swilling Mountain Dew. Ultimately, job done well, you are completely invisible.
Oh yeah, I forgot be in all places at once, look cute and smell nice.