The simplest (and cheapest) would be just to get an 8-track mixer and then run the stereo output of that into a usb audio interface.
Something like
this into
this.
(I've no idea if that mixer is any good, I've never used it. Behringer stuff tends to be not bad, but rarely great. The audio interface is great though.)
This set-up won't allow you to do any work on the mix after you've recorded, so you'll need to do a lot of work on mixing beforehand so that you get the sound right.