Wow, in my mind this entirely is driven by the style of music.
With pop|rock, I find the most useful chords are the right in your face but unnoticed chords. For example bar a G chord on the third fret and take the bar away and you have my favorite e minor when I'm working around the a minor at the 5th fret. Play the five Root F major 7 and take away the bar and you get my favorite a minor chord...
Seeing the chords as they sit across scales on the neck makes everything easy and combines horizontal and vertical at the same time. Play a root 5 A major and Hammer on two fingers to turn it into a b minor 7..Take a look at something ridiculously simple like Mike Campbell's intro to breakdown and the two Note cords are everywhere.
In a similar manner all the C, D and G style bars are extremely helpful. I avoid capos as much as possible and find lots of voicings that are as good if not better than capos with cowboy chords {Don't get me wrong.. some songs like Here Come the Sun really cannot be played without open strings and a capo}.
Actually, by far, the most important advancements around chords for me was learning hybrid picking. At that point you can pick any three note group and comp voicings that are far more flexible than six note chords. Just sit on a regular sixth root bar and move back and forth from the three high strings to the low three strings! In fact my favorite chords are usually passing tones and melodies where it isn't clear if you're looking at a c chord with a major seven passing tone or a C major 7... Of course they're the same thing it's just two sides of the coin.
Probably next important would be first inversions followed by second inversions across the neck. It's so funny how everybody knows how to put a C sharp underneath an A barr at root 5 4th fret but they Don't recognize the g first inversion 6th root on the 7th fret and and all its brothers and sisters moving up and down the front board.
In that same direction, progressions can be more useful than learning individual chords. Learn your ii V I all over the neck and you can improvise across practically everything in any style without having to think chords.
In the opposite direction, learning your diminished and half diminished chords is crucial for jazz and jazz pop. But once you jump on that boat, the chords start voicing themselves... you just need to follow the progression on that side of the neck. And this inserts well into practically any style of music.
And that leads to circle of fourths. Grabbing those progressions with two or three voices is unbelievably useful everywhere. Connecting jazz, pop, rock and country, it's probably the best way to interject inharmonic content that still sounds harmonic. 6th chords fall into that same category.
From there, learning minor 7, diminished cycles changes everything. You can sit on a single cord, loop around back to that same cord, yet sound like you went somewhere that was natural and harmonically complex at the same time.
Everything else is gravy... If you need a nine or a flat 9, just add it.
So now that I think about it, pretty much all of this is extremely useful in any style other than metal.
I use it as a warmup and I'd assume there is a tab somewhere. It's tough
