Before I start, I recommend that you read my article on Chord Families so that you know the terminology and stuff. Also, when I talk about the 1 chord, I am talking about the first chord in that family. You may also see a 2m chord, which means its the second chord in the family and its minor, or 7dim, which means its the seventh chord in its family and its a diminished chord.
As you may very well know, chords can be a great way to back up a song with a little rhythm. However, you can't just play the same chord over and over again (because that would be boring), and you can't just throw random chords together because some chords just don't go well with each other. I am going to show you two different types of chord progressions that sound good (because they're in line with music theory) and can be used for rhythm purposes. These are the 1-4-5 system and the 1-6m-2m-5 system. (the numbers represent the chords you use)
The 1-4-5 System
The 1-4-5 system is a pretty basic chord progression. I'll show you a 1-4-5 system chord progression in the family of A:
A D E
Yeah, it doesn't look very impressive. Anyway, in the family of A, A is your 1 chord, so you start with that (It's a '1'-4-5 progression). Next, you go to a D chord, because it is your 4 chord (1-'4'-5), and then to an E chord, because it is your 5 chord for the family of A (1-4-'5'). You can also substitute the 5 chord for a seventh chord, so E would become E7. Easy enough, let's go to the second way to make a chord progression.
The 1-6m-2m-5 System
You've probably figured out how to do this by now, but in case you haven't, I'll elaborate. Here we have the family of A again, but this time using the 1-6m-2m-5 system:
A Fm Bm E
Note that the 'm' makes them minor chords (the 2, 3, and 6 chords are always minor in a major chord family). So, first we have our 1 chord, A, then we have our 6m chord, Fm, then we have our 2m chord, Bm, and finally we have our 5 chord, E. Like the 1-4-5 system, you can substitute the 5 chord for a seventh chord.
I would like to give credit to "Music Principles for the Skeptical Guitarist, Volume One- The Big Picture" by Bruce Emery. This is the book that I used to learn most of this information. It is likely that there will be a Part 2 of this article coming, so be on the lookout.