Please forgive the "flourishes"... my analogy and the basic problem are running jokes in my circle and I couldn't resist.
First, the Signal-to-Noise ratio: what you were trying to record (like dialogue) is the signal, and the rest (background, etc) is the noise. That's about the only ratio that matters. There is also a thing called "room tone" that comes in before you're done; it's the ambient noise of the venue (very few recordings have actual silence.)
I think it's normal to start with the clearest track, the one with the best signal. As you know, as you amplify the track the background goes up too, so you'll probably have better luck with the best signal. You mention needing to reduce volume to "get it in range." I', guessing that that means the signal is loud but not clear? If the signal's waveform has lots of volume but is indistinct (the waveform is pretty much a wide flat bar rather than peaks and valleys) then it's called "clipped" because the peaks are clipped off. Clipped audio can be very difficult to "clean."
Irrespective of the type, the cleaning process is pretty much the same. We'll use Soundtrack since it's probably the only audio app you have.
Open the audio track of choice in Soundtrack as an audio file (not a multi-track project) and look for low, flat spots in the waveform. This will usually be background. If you cannot easily do this, just listen to the clip until you get to a "background only" point, the larger the better. Highlight this portion of the track and (from the menu at the top of the screen) choose Process>Noise Reduction>Set Noise Print. This captures a sample of the background noise. It is important that the sample have no dialogue because this sample is what we'll be trying to subtract. It's also better if the sample is a few seconds long.
Deselect the background and choose Process>Noise Reduction>Reduce Noise... to bring up the Reduce filter window. Here you can play back the track while adjusting the amount of reduction. There are some ins and outs here, so I'll ask that you read the appropriate sections of the on-line users manual available in Soundtrack's Help Menu.
This is seldom a one-pass fix. Actually it's not a "fix" at all (remember, the chicken is dead...) but a partial adjustment based on what little audio you have available. If you overdo it, you'll hear the audio go "glassy" (the voices start to quack) which is an indicator that you need to back off a bit.
After you've done your best, some times you can get an extra yard by mixing a couple tracks together. Another technique is to manually reduce the gain in larger sections of background. This is where Room Tone is needed to avoid complete silence.
That should get you started...