That sounds like a great opportunity, Greg! I've tried it, and it is a lot more difficult than it seems, as I'm sure you know. This stuff might end up being like telling Julia Child's daughter how to bake a Duncan Hines cake, but you asked....
First, as noted above, avoid relying on the feed from the sound board. The sound board reflects what needs extra amplification, not every sound you hear. Also, keep in mind that even with over-the-ear headphones, the recording will not sound like what you hear from the board, even if you tap into the seperately-mixed feed. That makes a sound-check before the show irreplaceable to work out any kinks in the mix. Take the sound-check CD to your car or re-play it over the sound system to verify that the mix sounds well-balanced.
Second, on a related note, use as many mics as you can. Many of the acoustic things that you hear in the room during a live show are not amplified and are not miked, so they won't show up on the recording or will be under-represented on the recording unless you purposefully add mics. Especially drums. Drums need at least four mics: a kick drum mic, high-hat mic, and two condensor mics over the top of the set to catch the cymbals and other drums. All of them can be rented very cheaply at sound equipment stores (like $5 per mic, including cables and stands).
Also, I suggest including one or two high-quality, ambient condensor mics in the audience or way above the band to capture the effect of how the sounds blend together in the entire room, as opposed to how each individual instrument sounds when miced very, very close-up. Without the ambient sound mics, the sound becomes more "canned" and loses the richness of a live performance.
As for the recorder, I would not rely on the Windows recorder. The Windows recorder seems much more geared toward taking voice memos than recording music. Using a software program would be the only way to record seperate tracks on your computer, which is necessary to be able to adjust the levels afterwards.
As for the recording medium, I recorded directly onto a CD burner, using a minidisc as a back-up. I rented the CD-recorder from the same place that leased the sound equipment. No software necessary, but the recording is one-track, so you lose the ability to adjust the levels afterwards. But if you don't find the software, it at least gives you an option besides the minidisc. It's like recording on a cassette tape, except you can't erase: just press "record" and it records. You can edit the length of tracks afterwards with Nero.
Finally, as I'm sure you know, there are lots of post-recording digital editing software products out there that can normalize pitch, synchronize horns so they are together, and otherwise adjust and alter the recording to eliminate many snafus. I have not used any, myself, but I have seen them work and they are amazing.
Best of luck. Should be fun.
