How do you choose this EQ or that compressor

just through trial and error, hopefully not to much error, but by using your various options, over time you will know, get a feel that x plugin will suit x situation. let your ears decide, for example certain compressor might shine on the drums, or bass, while another will shine on vocals, eventually you get to know. then there is other influences, ease of use, cpu drain and on and on which may influence your choice. sometimes you may just try another option than your usual and really like it for that situation, it may even become your fav for a while. i have had a habit of just reaching for valhalla room reverb for guitar bus, recently just threw on rematrix, had a play around and found i liked that, not that it was better or worse, maybe just different, but at that time, the project, the mood i was in, whatever, it ousted my usual pick, variety is the spice of life they say, although to much choice can sometimes be a curse. that's just my thoughts anyway, ymmv

Learning which plugin is best for which instrument is a huge undertaking but I have found that if you will solo the track and step thru the different plugs you will find THE one that really does improve the feel and attitude and the sound of the track. Solo that strat track and listen to it by itself and you will clearly see the difference in what each plug does. To me, it is very hard to have all the tracks playing even in Dim mode and really hear what that plug is doing for each instrument.

Hey Schwa,
Choosing an effect all comes down to coloration.  Practically every DAW now come with effects that can easily make great sounding recordings using only what they come with.  The secret is in getting to know what each one does and determine what to use by the function you need it to do.  For example, find out which EQ you have can that can high pass tracks that don't need 80hz like overheads and use that.  Find which delay you can use as a slap that allows you to time to tempo.  Find which reverb has a great sounding Hall preset and use that on your Room bus.  Simplify and narrow your choices until you become more familiar with your system.  Then you can go crazy with outside plug ins.  
I use onboard Sonar effects both through the ProChannel and inserts along with Waves, UBK, Slate, SoundToys and freeware on my productions and I'm still learning.
I could suggest you look into a course like the ones offered on Groove3.com to learn more about effects and how they're used.
Then the decision process becomes manifestly easier.

My criteria, in order of importance...
 
1. Ergonomics. I gravitate toward effects that are quick and easy to dial in. ValhallaDSP reverbs are a good example. Simple, functional interfaces that don't get in the way. Resizable UIs (e.g. Melda and Fabfilter) are a big plus. Knobs that respond to the mouse in intuitive ways. The ability to type in values. Controls that aren't hidden. Controls that are clearly labeled as to their purpose. Labels that aren't too small or low-contrast, that can be read in low light. No pink or lime green. 
 
2. Functionality. If you're going to invest the time to deeply learn some piece of software, you want it to be versatile enough that you won't need to learn too many alternatives. Ozone, for example, is an all-in-one mastering tool so full-featured you don't need anything else. Pro-C does everything a compressor can be expected to do, and also satisfies requirement #1. One-trick ponies have a place, but they have to satisfy #1 or #3.
 
3. Unique tricks. Sometimes an effect has an unusual capability or characteristic that makes it uniquely suited for a particular application. FabFilter Timeless isn't as simple to use as other delays, but its unique modulation features assure it a position on the first-string roster. Fabfilter Saturn isn't as versatile as other alternatives, but it has capabilities no other distortion plugin has. Meldaproduction's MSpectralDynamics does just one thing, so it fails #1 and #2. But that one thing that it does is special. 
 
Surprising things that are rarely a factor: sound quality and aesthetic appeal.
 

The QuadCurve's four different curves demonstrate how EQs can sound different depending on what they're designed to do. I've found the easiest way to evaluate EQs is to feed noise through them, and you'll hear the difference between, for example, what happens to Q as you change gain with different curves. I wrote a "Friday's Tip of the Week" (Week 59: Understanding the QuadCurve—Why Noise Is Your Friend) about using noise to help understand how EQ affects a sound.

Don't want to get into all these different preferences but to add on what WST3 stated, one must know how to use each tool and what makes one different than the other.  The only thing that can give you this knowledge is experience and some teaching from other sources (other engineers, the internet, books, other recordings, etc.).  But still, even with the teachings, experience is the only way to really understand your tools and what makes each one different.
 
Understanding SOUND is also important... one of the many things that took me awhile to get my head around was you really can't add something that isn't there in the first place (with EQ) but you can take out some of which is there.  So, how you record the track is as important as how you mix the track.  And the other important thing about compression is how the attack and release work together and then how each unit has different characteristics. For example, you can compress the AIR out of a track without slamming the input gain easier and more effective on some compressors versus others. I would say that the 1176, DBX, LA2a and LA3a, Fairchild and a few other vintage compressors are easier to use and as such easier to gain experience before starting with the more advanced modern compressors like the MANLEY and the VSC. 
 
Like most things, it is best to start with the basics and build upon your own knowledge.
 
IMHO
 
 

jimkleban
Understanding SOUND is also important... one of the many things that took me awhile to get my head around was you really can't add something that isn't there in the first place (with EQ) but you can take out some of which is there.

So true! Especially the part about you can't add what isn't there. You can subtract everything else to make it look like there is more energy in a specific band, but that's it! (Exciters can, in fact add, but that's a different topic<G>!)
 

jimklebanSo, how you record the track is as important as how you mix the track.  

That is the place to start! I was really fortunate that one of my mentors emphasized (over and over and over) the importance of microphone selection and placement. These two words were always used together, the microphone you selected affected the placement, or if you had limited place to position the microphone that would affect selection. Two sides of the same coin.

Which make sense, but the thing that made his recordings remarkable was that he used selection and placement as the first stages of equalization and dynamics control. He would not reach for a knob until he had the microphone exactly where it needed to be. That lesson still sticks with me on those occasions when I am fortunate enough to record live players!
 
The analog to that would be selection of synthesizers or sample libraries, and even specific patches. You don't have as much control (the developer made most of the decisions for you already), and it does get expensive, but that's what we have to work with when we turn to virtual instruments.
 

jimklebanAnd the other important thing about compression is how the attack and release work together and then how each unit has different characteristics.

 
Read the manuals, or look at the front panels!
 
The Urei 1176, for example, has a fixed threshold, you determine the relationship between your signal and the threshold by adjusting the input level. Pretty cool really! First, it means you can use that input stage to color the sound, second, when one designs a compressor there are all sorts of trade-offs to be made (e.g. feed forward or feed back, variable gain or attenuation, and so on.) Choosing a fixed threshold left Mr. Putnam free to address some of the artifacts from earlier designs with different solutions. So the 1176 behaves quite differently than the dBX 160 because Mr. Putnam and Mr. Blackmer had very different approaches to the problem.

When I use an 1176 I first "calibrate" it - habit I suppose, but I set it up for unity gain with some small degree of gain reduction, then I know what's going to happen when I spin various knobs or push buttons. I can, for example, increase the input level and decrease the output level to maintain unity gain through the device, but by doing so I'm also changing where  the input signal crosses the threshold.

It isn't as easy to do that with the dBX 160, so my approach to that is to set the threshold to the maximum and set levels accordingly, then start to apply gain reduction by way of the variable threshold.
 
That's where I suggest folks start, set the attack and release fast so the level changes are really audible and play with the threshold. Then start to play with attack and release times. Which is an entire topic in and of itself!
 
Last thought for now - equalizers also have  quirks! The Valley People Maxi-Q placed the filters in parallel, while most other parametric equalizers place them in series. So they operate differently, believe it or not! One of my favorites, the Maag EQ4, has a band that exceeds the audible spectrum by a couple of octaves, it tends to sound really smooth. There are lots of little tricks like that!

Time spent with an experienced engineer is still the best teacher, but there are some reputable courses out there. When asked I recommend Dave Moulton's Golden Ears.