Chords are based on scale steps - in C major that would be -
C D E F G A B C
If you use the number system, most chords in a song are on -
PRIMARY CHORDS
I, IV, V
1 4 5 (in C - C E G, F A C, G B D - like in 'La Bamba')
Think of these like the primary colors, red, yellow, and blue.
Of course there are other colors in between, like purple, green and orange -
MINOR SECONDARY CHORDS
II, III, VI
2, 3, 6 (in C - D F A, E G B, A C E)
And the half-diminished chord - on step 7 -
VII
7 (in C - B D F)
These are 3-note chords - Triads. When Jazz players talk about 'color tones' they are referring to adding or altering extra tones to these chords.
There are lots of books and courses on Jazz Harmony and Theory, discussing chords and soloing on major, minor and other modes. But you asked about progressions...
Most chord progressions are - you guessed it -
I, IV, V
1 4 5
That is, they typically move by fifths/fourths - C to F to G, etc.
Less common (more common in R+B/Gospel) are the secondary minor progressions, usually taking the 'scenic route' to get to the Major key - like -
VI II V7 I
6 2 5 1
and lots of other progressions you can find on LGM.
BTW, Major/minor are related - the relative minor scale begins on the 6th note of the Major scale. That's why a CM6 chord is the same as an Am7 chord. Weird, huh?
Chords can also move up or down a scale step (2nd) or a 3rd or 6th. Less common (but really important to what I think you may be looking for) are Chromatic progressions, which slide up or down out of the scale a half-step between the main chords - those 'passing chords'.
The main important chords in a song tend to be on the 1st and 3rd beats, and passing chords tend to be briefer, happening shortly before the main chord changes. IMO, the big thing is to get the main chords in a song down first, then add passing chords later.... I often tell guitarists this, so they don't have to deal with too many chord changes when learning a song...