Typically, you would interview several engineers who did recordings you've heard and liked, and see who you get along with and fits your budget. It could be that they recommend a hybrid technique, such as giving everyone a separate mic, but recording directly to stereo and only editing as needed to get to CD. Or they might prefer to multitrack, but it usually costs much more and takes much more time. It could be at a studio or on location. You'll learn lots if this is your first project - ask as you go, most folks are glad to tell you what they are doing and why.
Sadly, many people with a computer and a few mics think they know all about recording all types of music, and they are almost always wrong. I would look for recordings you like and see who did them, even if you have to reject them for cost, perhaps they'll have other referrals. Also, try asking local classical groups or colleges about recordists you can interview. Acoustic music such as yours is a different matter than a punk grunge band.