I wish had a good suggestion based on experience of doing the same, but I don’t (I just plug in when I use sound reinforcement). If you are looking for a great condenser for just your guitar, a Shure SM81 is worth a look. It has a -10db pad switch which would be handy for live. I am guessing that if you are mic-ing it for live reproduction through an amp, a condenser mic might be tough to control the feedback. I picked up some uber-cheap MXL condensers and they are quite nice for recording, but I am guessing they are way too sensitive for live work. If you are looking for a central mic for multiple instruments and voices, I think many people often use large diaphragm condensers (like an AT4033).
I’m sure some others will hop in with some good suggestions.