I played around with Minor Chords and made a Chord Progression. The focus is a lot on Minor Chords but as I resolve on an F major I guess you'd refer to it as F major progression? Anyway, here's what I played:
My Progression goes I - vi - V - ii - iii - IV
The first Chord is the F, next I play D minor. After that I play a C in the A shape and a G in the Dm shape, but I play this one as a triad (correct, @[477:@Ids Schiere] ?), without the bar on the fifth fret. Next I play an A minor in the Em position and then a B flat, connecting nicely back to the F.