One more important question: do you plan to record openly (with permission of the venue and musician), or stealth (without permission, typically requiring much smaller gear that is easily concealed)?
The answer will make a big difference in the gear people recommend. If you intend to record primarily openly and can use full-size microphones, there are plenty of mic options in the sub-$800 range. If you intend to record primarily stealth, there are far fewer options.