It is a quite different approach to combine a mixer and a recorder, and most likely one of the simplest solutions around.
There is plenty of compact mixers with a 2 channel usb interface around and some even have a full fledged 16 i/o firewire interface.
The Cymantic LR-16 has 16 ins and 2 outs and is a stand alone 24bit/44-48khz recorder. (you just add a HD or thumb drive via USB). Or it can double as a 24bit/96khz USB audio interface.
It is fed from the inserts of your mixer with regular TRS jacks to hardwired inputs. You do not need to arm the right tracks but just hit the record button, simple.