Here's a new trip: what if you look at all the notes you play as intervals in the key you are playing in?

The 3-6-2-5-1 progression is derived out of one base scale.  For the Major progression, it based off the Major scale.  All the notes of all the chords in these progressions are prescribed to fit this scale.

This pdf shows the guide tones for each change in the 3-6-2-5-1 progression, from the perspective that they are intervals of the tonic (root).

If the five chord of C is G7, you could learn the notes of G7 (G - B -D - F) be the following:
5, 7, 2, 4.

Those are the chord tones of G7 as intervals of C Major. The essential guide tones are 7(B) and 4(F). You could do this for any chord.

Guide tones are essential tones in your solo to “cite” a backing chord. The guide tones for a chord start with their 3rd and 7th.  These tones distinguish between Major/Minor and Dominant.

Many jazz standards move in fourths, any chord is likely to use the circle of 4ths as its “roadmap” to resolve back to the root chord. The 3-6-2-5-1 is just a progression of fourths starting all the way out at the ‘three’ chord.

For this progression, the intervals of the essential tones for all these changes are:

Major:

3:      5, 2
6:     1, 5
2:      4, 1
5:     7, 4
1:     3, 7

Minor:

b3:     5, 2
b6:     1, 5
2:     4,1
5:     M7, 4
1:     b3, b7*

*The thing about the Minor progression is it is based on the Tonic being a Minor with a Major 7, but everyone in jazz plays the min7 with a b7.

By learning the inversions of a chord, you will learn new fingerings and ways to play the same chord on different parts of the neck.  This will give you a greater vocabulary for your comping.