The 424mkII will record 4-tracks in direct mode. Direct mode recording records the Input/Channel strips 1-4 directly to tape Tracks 1-4, respectively. Direct mode recording is not rocket science. Whatever's on Input/Channel 1 records directly to Track 1, and so on,... 1-4. Given that you have 4 members and a vocal PA, it gets to be an uneven equation, as to how to squeeze all these parts onto a 4-track recorder, using only 4 Input/Channels.
SO,... what that really means, is you'll have to pair two or more parts together, and a lot of your success depends on experimenting with what works best. I could give you some hypothetical setups, but it's hypothetical, at best, and still needs to be proven or disproven in the studio.
F/I,... decide which parts you can pair up together onto tracks, such as:
Bass paired with Drums, or Sax paired with Vocals. Use your best judgment, as to which parts would fit together on a track, and not crowd each other out.
So,...
Input/Channel 1 to Track 1: Drums, (with a single mic).
Input/Channel 2 to Track 2: Bass, (either DI or mic-on-cab).
Input/Channel 3 to Track 3: Guitar, (either DI or mic-on-cab).
Input/Channel 4 to Track 4: Vocals and Sax, (using a single mic to pick up vocal and sax elements, together).
This setup example keeps your drums, bass and guitar separate, which is something that will be beneficial in the mixing phases, and makes the assumption that the vocals and sax will not be droning simultaneously, but maybe will work opposite each other, in most cases, providing vocal and sax with their own "space", despite being crammed onto the same tape track.
There could be other formulations, depending on your best judgment, as to what works best in studio trials. Also, if you have a small submixer handy, the equation gets more complex, and simpler at the same time, with the submixer handling some front end mixing of elements, that the 424mkII itself cannot adequately handle.
THAT's ALL A HYPOTHETICAL EXAMPLE, above, but from your description, it seems that it might be the optimal setup. That's not for me to decide, though, as you should try a few different configurations out in the studio, and use what works best.
The only way to improve on that example, is to go out and score the Tascam 388, and go 8x8 direct to 8-tracks on tape. Since you just got your 424mkII, and are learning the ropes on 4-track, plus budgetary concerns, I'll keep my suggestions focused on the 424mkII and 4-track. Otherwise, my next suggestion would be to step up to 8x8 mixing and 8-track recording, that is, the Tascam 388,... which is a long term goal for growth, I suppose.
Good luck!!