A single mic sounds like an attractive idea, in its simplicity - but it may well prove much harder then you think. If you want to pursue this idea I hope you will find an expert to talk to who does support the idea, and has some expereince with the technique to pass on. And I wouldn't believe an omni directional mic is appropriate.There has been some very good discussion that touched on this subject, recently in this thread. I hope you pull it up and read through it. Much of the discussion centers on amplifying acoustic guitars, but there is some learned focus on mics, and mic placement, as well.
Finally, I suspect that the reason people consider using one mic on stage, for choral, and bluegrass music - is the attempt to keep a 'natural sounding' low noise stage. That is, playing together in an acoustic setting, a group of musicians may well acheive a balance that works for them, yet when they perform on an amplified stage, that balance is lost. Wishing to transpose the non-amplified 'environment' to the sound stage, we hope that a single mic 'listening' to the otherwise acoustic performance will reproduce that natural sound. I suspect doing so is much harder then you think. I likewise suspect that learning how to amplify everything well, can recreate the more natural sound you seek.
Learn how to mic/pick-up each instrument. Mic each voice. Place the house system well out in front of you, and learn how to avoid reflection of that house system back onto the stage. Place monitors correctly on stage, so all can well, but none are loud or overpowering. I think the key to achieving the enviroment you want on-stage is keeping the stage noise down to a minimum. Learning how to use a sound system is the only way to make that happen. If you are successful at using only one mic, I suspect you still have to learn how to use a sound system.
Many musicians don't have the time, inclination or interest - to learn about sound, They see it as a neccessary evil. And that's OK - but you'll need to find an additional member, (even if he/she is an occasional) member who is a sound system expert.
I've seen very very talented musicians sound very very bad, and loose the audience immediately - because the sound system was so poor, or poorly managed. I've also seen not-so-very-good musicians win an audiences favor becasue they could use a good sound system, and they had a little bit of showmanship.
Good sound is crucial to the success of a performance.