The big challenge you'll face with that many USB mics into one computer (regardless of what the OS is) will be getting the computer to recognize each microphone individually. This'll likely be an even bigger challenge with Linux (tho I have no real experience with Linux, so I could be wrong). MacOS allows for the creation of something called an audio Aggregate Device that can help with using multiple USB mics with a single computer. But it doesn't always work. I realize you're not intending to use a Mac but I'm pointing this out here to show that even a commercial OS with lots of bells/whistles doesn't do multiple USB microphones very well.
As far as using Audacity, it's the best DAW I know of for Linux. But again, I have no practical experience with Linux.
If it were me and I was trying to solve the same problem, here's what I'd suggest. Get an audio mixer with a built-in USB interface that has been proven to work with Linux. Order some Audio-Technica ATR2100 dynamic microphones. The 2100 is widely regarded as a good-sounding but inexpensive mic. It can also do either a direct USB connection to the computer or switch to an analog XLR connector to be plugged into a mixer.
I also recommend asking your question in these online groups where they may receive more feedback from people who've tried to do what you want:
https://www.facebook.com/groups/PodcastCommunity/https://plus.google.com/communities/102333709604116814839Good luck!