It might depend on whether you are thinking about a particular "instrument" (including vocals) or whether you are thinking about the stereo bus.
In general, though, I think many mixers will start with EQ and/or compression. (IMO, these are really the foundational tools for mixing, other than just levels and gain-staging.) Admittedly, you will find people who like EQ before compression, or EQ after compression, or sandwiching multiple points of EQ and compression .... It depends on the mixer, the source material, what the mixer wants to achieve .... You can find a lot of discussion online about these issues. Placing EQ before compression obviously emphasizes compression of any boosted frequencies (or deemphasizes compression of scooped frequencies), while compression before EQ smooths out the existing sound and then boosts or cuts from there. A lot of people will make small EQ and or compression moves with multiple EQ or compression units. Or, for compression, there will be a fast compressor to catch and tame peaks in a transient-heavy signal, and then a slow compressor following it to smooth out the results more evenly. (An 1176-style compressor to catch peaks followed by a more languid LA2A-style comrpessor is a classic combination.)
Then, I think more "effecty" things like delay, etc. are usually after the "basics" of EQ and compression -- and often placed as send/return effects on aux channels. But, of course, people will often compress or EQ signals going into delay, reverb, etc. EQing (but, I think not so much compressing) signals coming out of delay or reverb can be useful, too.
But, in the end .... as DarkStar says, there are no "right answers". Different situations, sources, and objectives may call for different treatments. I've found it helpful to try out different techniques that I see people using online (in YouTube videos or whatever) not so much to achieve the same thing that they are trying to achieve, but really just as a vehicle to get to grips with what the tools
do. Then, as I get better with that, I can get closer to being able to apply that absolutely-true-but-not-always-very-helpful-advice that people like to give about "using your ears"!
All that said ... There are things that I "tend" to do on particular instruments/vocals, or the stereo bus, etc. Vocals get a mix of EQ and compression (very often the "catch fast peaks" followed by "heavier but slower" treatment); I'll then send the results off via sends to parallel compression and delays and stuff (often EQ'd/compessed going in to those). I don't like a lot of reverb, but might send delays to a light reverb. Drums likewise get EQ and compression on different elements of the kit (kick, snare, toms, hats if separate, overheads), maybe some reverb for the snare and/or toms, and then maybe heavy parallel compression for the kick, snare, and rest of the kit separately. Bass is often split into a heavily compressed clean (DI) low-end signal (maybe 200-250 hz and below) and a high-end signal (i.e. 200+ hz) that can be amped or otherwise messed up
and then I bus those back together for some further light compression and EQ (just to "glue" things together). Guitars ... I generally bus distorted rhythm guitars together for some EQ, but seldom much compression (maybe some judicious multiband if they are chuggy and there is too much "woof" down there). Lead guitars the same, but usually processed separately.
On the stereo bus, there are some compression plugins set
VERY lightly, providing more saturation than anything, as well as some EQ to give a
bit of "smiley face". I tend to have some channel/aux presets set-up that I use, but I honestly don't recall the ordering of things.
It does change, from time to time .... Basically, I like a little compression and EQ to "mix into", but nothing too crazy.
And I'm sure many people could look at what I currently do and screech "That's dumb!" or "That makes no sense!" and they would probably be right!
But I like to think I'm sucking a little less this year than last year.
by DrRobF » Wed Sep 18, 2019 4:59 pm 
I've just have been a newbie long enough that I've collected some notes from actual experts. 