Let's make our chords more sophisticated for this 3rd progression. Open string chords aren't going to cut it any more. In this version we still use minor 7th chords but we're going to move up the neck a little and use shapes more usually associated with a jazzier feel.
The first thing to note about our new shapes is that we have a gap of one string between our bass or root note and the rest of the chord. This separation exists to allow the chord to breath a little better. Chords sound better if we spread the notes out a little allowing each note it's own space in the voicing - this is particularly effective when separating the bass note from the rest of the chord.
The other point of significant note is the new A7 chord in bar 4. This is a very common device in bar 4 as an A7 chord leads very effectively to a Dm7 chord. Try it yourself and you'll hear the results are very pleasing. Again, at this stage the theory is not so important, just getting the sound in your head. You'll come to expect this sound after a while!