Another vote for the Zoom H4 or H6.
We're getting very nice results for live recording with the H6 stereo mic set to capture the drum kit and the mid-field of the backline (amps and some vocal monitor), then running direct lines in to other tracks for vocals, kick drum, and a mic set to capture the backline amps better (bass and keyboard amps). The H6 has another line in, we may close-mic the guitar amp to get better level control on it. Of course all of the lines have plenty of bleed, but the different lines are giving us much more control over the final mix, and we're not noticing any phase issues, probably b/c the mics are all pretty close together on the tiny stages we play on.
For mix down we're dumping all the tracks into Audacity, which is free, and mixing from there. For simple mixing and minimal post-processing Audacity works fine. If we ever get a performance we really want to treat right we'll use a better DAW at that point.