In my Macintosh environment I have done audio replacement and editing with iMovieHD - which comes bundled with the Mac (so, "free"):
http://vids.myspace.com/index.cfm?fuseaction=vids.individual&VideoID=14690627
In this particular example, camcorder mics (actually, the stationary safe shot camcorder used internal mics; the other camera used an external mic - though that was not necessary) were used during the session and everything on stage was connected (direct box or mic'd) to a DigiDesign ProTools set up. After the session, the audio engineer mixed the ProTools captured audio and sent it to me a few weeks later. While I was waiting for the audio mix, I was editing the video. The final mixed audio was posted at YouSendIt.com and I downlosed it. This AIFF was brought into iMovieHD, sync'd with the existing audio, the audio that came in from the camcorders was muted and the final video and audio was exported as various computer readable compressed video file formats for posting or online archive, to DVD for playback on a "regular" DVD player and back out to a miniDV camcorder as the miniDV tape is the long-term archive. The camcorders used were a Panasonic DVX100B and Sony HDR-HC1 - both were in standard definition, 4:3 aspect ratio.
In this example,
http://vids.myspace.com/index.cfm?fuseaction=vids.individual&VideoID=7382678
it was a live, single camera, shoot that used an Audio Technica AT-825 connected via BeachTek DXA6-A to a Sony HDR-HC1 - so lots of camcorder and XLR adapter manual audio control was available - and the house audio was captured - no external capture/replace. Because the camcorder (and mic) were on the right side of the room, you may notice the audio is slightly heavier on the right audio channel. I *could* have fixed this in post-production or done a better job during the capture... an alternative would be to place the stereo mic in the middle of the room (but that could get in the patrons' way - unless I had a way to suspend the mic from the ceiling, which I could not do).
I very rarely ask the audio person for a direct board feed. It is a hassle, you need the right cables and it assumes the audio person knows what they are doing because they need to mix the house and the discrete AUX sends very differently.
The ProTools rig allows for each instrument to have its own track - but is a pricey solution that many folks don't have access to. It can provide "studio quality". The part that makes this pricey is also the part that you need - that is, being able to get the information from each individual audio source onto is own track... then that data feed (usually via firewire) populates the "master" audio file. Mackie has good boards that can do this, too - and they have software - for the audio capture part. Again, the individual track for each instrument is the deal.
If you are merely capturing stereo, there is nothing to "mix down" later - other than perhaps some correction and normalizing and fade-in and fade-out... and adding applause. If this is the case, then pretty much anything with manual audio control and stereo mics will work just fine. That is where the mic placement comes in... and connection to a field recorder like those from M-Audio or Zoom or Marantz or Tascam or Fostex or Sony... Some of these include a built-in stereo mic that is quite good, so no additional parts/cables/$.
I prefer picking up the audio with the camcorder (whether it is used in the final video or not) - during the audio sync with the external audio source, when you are off a a frame or two or three (or more), there is "echo" so when that echo goes away, you know the audio is sync'd.
In the film world (or REALLY high end cameras that do not capture audio), they sync by using timecode... Newer slates connect to the audio field recorder with a cable and the timecode is recorded to the video or film. In post production, they mach up the timecodes from the audio capture and video capture device. In the film world where the film camera does not use timecode, they use a slate to mark the scene, and when the clapper hits the slate is when the audio capture device records that audio... I really don't think you want to (or need to) go down this path. Some Fostex field recorders can use time-code enabled slates - most low-end field recorders cannot connect to a time-code enabled slate.
When I got FinalCutPro, it came bundled with a bunch of software - including FinalCut (mostly for video editing, but provides some audio editing capabilities), SoundPro (very heavy audio editing) and some other tools for making titles, DVD authoring and effects. All the apps in this post run on Apple Macintosh OSX. I expect there are similar tools available for other operating systems. I also use Audacity (with is open source and cross platform) for some audio editing...
Anyway.... since I don't know the environment you are in, and I don't know what audio recorder you are using, my ability to make recommendations is limited... but to make things easy, I would start with the easiest: Don't use the PA mixing board into your audio recorder. Get the house audio using well placed, decent, condensor mics (for stereo) or a decent stereo mic and connect them directly to your audio recorder. If you want "studio quality" audio and control of the individual instruments/audio sources, you are getting WAY more complex, will need more gear, more skill more tools (hardware and software)... and that means more $$$.