There are more than a couple of mixers compatible with Linux around. Don’t go for Behringer Q802USB or any of the Xenyx series because you will get stereo (2 channel) USB interface only. The real mixers with multichannel USB interface by Behringer are the likes of Behringer X18, X Air XR16 or X Air XR18, all of which have a native control software for Linux. There is also popular Behringer X32 Compact, but it is priced some 50% above your budget.
Some members of this forum had success with Presonus StudioLive AR12 USB and Linux and there is also some new addition from Zoom, the Zoom LiveTrak L-12 which a member of Harrison Mixbus forums reported to work on Linux with some instructions:
PC and L12 powered of
Switch the “Class compliant mode” to “ON” on the back panel
Select the preferred bit rate on the switch on the back panel
Plug in the USB cable that came with the L12
Power on the L12 and then power on the PC
In “JACK” select the same bit rate as on the L12
In “JACK” select the L12 as audio in and out
Specify 14 channels(12 + 2 master ch.) in and 4 channels out.
Restart “JACK” and you ready to go tracking/recording
There is a lot of choice for the band recording, I hope you find some of it adequate.