Hi Schwa,
One way to approach that question is to think about various fx, both hardware and software, the same way you think about microphones. For example, if you're micing up your D28 you could probably make it sound OK with your 57. I mean, enough time spent with positioning and then the right EQ and it'd probably be OK. But why? You have your SM-81's sitting right there. You've probably used them on Ac Git a million times. You don't have to spend time messing around with them, they just sound good. Now, do you use spaced or coincident pair? Well, if you think there's a reasonable chance of needing to collapse to mono, probably coincident, but beyond that, they have different sounds. You've probably mic'd up your Martin a ton, you know which mic setup gets you a particular result and that's the one you go with.
Now, apply that to compressors - yesterday I was doing production on a vocal track. It was a male singer, not terribly bright sounding, doing a kind of funk song with fast lyrics. I could have gone with my TLA-100 (an LA2A-style compressor) or one of my 1176's. From a purely technical standpoint I knew that the TLA-100 was a bit too slow to handle the pace of the lyrics and the associated transients. From a sound standpoint the emphasis on the upper-mids from the 1176 sounded great. I could have probably gone with the TLA-100, and with some tweaking and whatnot it would have been OK, but the 1176 was right there, so may as well just use it and save the headache.
For your question about "go-to" tools, the answer for me is "sort of". I have tools that I know and like for particular applications, and then another sort of general set of tools for general tasks. Again, back to the microphone analogy - imagine you have a guy coming in to record an instrument that you've never heard of....maybe a hurdy gurdy or something. You probably have one or two mics that, generally speaking, are pretty tough for stuff to sound bad on, so you slap those on some stands and start there. Maybe after you hear the first take you break out the SM-7 because you know it does a particular thing when used a particular way, and why mess around at that point? I think most folks get to a point, if they do it enough, that fx become sort of like that.
Hope that helps,
Dean