All you need to remember are basic chord structures, the rest is filler.
Start on the tonic, I, and then progress to IV or V. those can be reached by any of the other chords, it's up to you. To end a phrase, generally a V7 to I cadence is used. vii is a diminished leading tone chord and typically goes back to I or V. V to vi creates a "deceptive" cadence. Playing progressions backward doesn't help lead anything forward.
There are also several rules: avoid parallel fifths to keep motion going. use parallel octaves only if reinforcing an idea. and make sure your leading tones resolve; half of chord progressions is just that. listen to where the notes go and follow. the half step leading to the tonic is called the leading tone.
I - IV -V - I is the most typical, fill it in with other chords:
I - ii - iii - IV - V - vi - viidim - I
i - IIdim - III -iv - V (the g is sharped to lead into a in an a harmonic minor scale) - VI - i