You do bump into one problem almost immediately. The M-Audio stuff is very nice, but they typically use ASIO software drivers and Audacity doesn’t support ASIO. You can try it anyway, but, there are a lot of postings from people who say, “I have an M-Audio [some part number] and it will not [some complaint]”
It’s always something odd like missing one channel or distorts the sound.
The SM57 is a very nice microphone, but it’s professionally balanced (three gold pins on the bottom) and it needs to match the sound card.
I can give you pieces, I guess. We use these “cute” Peavey mixers at work and they seem to run well.
http://www.peavey.com/products/browse.cfm/action/detail/item/115024/PV(R)%206.cfm
The application is one or two people sitting at the front of a room giving a training lecture with one microphone in the audience for questions. The mixer directly supports four microphones, as well as headphones to monitor the performance and a simple equalizer.
It’s an analog device, so we cable it into the Line-In (blue) socket of a large, deskside computer to record it. It will also plug straight into a Mac. It will probably not plug into a PC laptop without one of the other USB soundcards in our list.
https://forum.audacityteam.org/t/sound-card-reviews/8375/1
Whatever you pick has to say in clear English, “Stereo Line-In” or “Stereo High-Level In.”
With all that, it’s never going to sound like a Recording Studio. The system does have a very gentle background noise (hiss) and I’m sure if I measured it, it would have some small distortion, but for the bux, this should totally do it.
You will probably never have to worry about the quality of the mixer, because the quality of your room is going to be far worse. I lucked out in a big way. The first family that moved into my house had a son that played drums. The small third bedroom is soundproofed.
Koz