been many years since I was in a band doing this.
Back in the day, being in close proximity to a music city (for me it was New York City, and Atlanta), we'd just ask other bands doing similar music for recommendations; buy other bands tapes/CDs / look at recordings of other local/regional bands doing similar music, and seeing who worked on other bands' recordings and the quality of the work; asking around, and within "genre circles" you'd often hear the same names and places come up. Keep a list of names and roles, and what bands they recorded, mixed, mastered, then start reaching out to them.
You can look at who did the recording work for more successful bands in your genre too; and start to see who is used more frequently, and where they are located,...but this was always more expensive as they were in demand, even if they were working locally to us.
With today's technology you could record your tracks yourself, wet and dry, take a sample song to a mix engineer; or talk to mix engineers to see what inputs they need. I think if you can record your own tracks, finding / using a Mix Engineer and a Mastering Engineer is all you need. Most Mix engineers will know mastering engineers, some do both.
hth
Good luck!
