I haven't played a banjo before, but I hope that some guitar knowledge may transfer.
Choosing chords comes down to which chord comes before, and which chord comes after. At a beginner level, it's likely that you only know one or two forms for a chord, so this decision is easy to make. At higher levels you can play inversions in very strange paces on the neck, allowing for more variation. This will let you find chord sequences with no massive jumps, and the hand moves small amounts up or down the neck between chords.
It is very easy to change between open string chords. They are all in the same position on the neck and you have no barre to deal with. From the diagrams you have, you are only using open string chords.
At a beginner level, changing between chords is slow and painful. Placing each finger individually and looking directly at your hand while doing this will slow down every chord change. With practice and practice alone you will learn to change chords without even looking at your left hand. This will drastically reduce changeover time, making it possible to change between completely unrelated chords quickly in open positions.
I won't go into bar chords here, since they do not appear in the question.
Regarding the song in the example
Most of your chord choices are fine. Your G7 can be played with fingers 2 and 4 so that they don't need to move when you press down 1 and 3 to play the D7. You then lift them up again for G7. Changing to F7 is a simpple matter of moving 2 across a string, and sliding 4 down a fret. The other fingers simply press down where they are needed.
There is now a massive jump on the neck, moving up 4 frets. Lucky for you, the next chord actually uses all four fingers on the same strings, so its a simple "slide up and readjust" chord change which won't interrupt your playing once you get used to it.
Going to the B7 and back to the E7 could cause a hiccup if done incorrectly. YOu could simply slide the fingers up again, and move the fingers to the correct frets on the same strings. This results in the first finger being behind the second on the same fret however, which is not optimal. I would suggest to lay the first flat over the middle two strings for the B7, and then do the change in reserve on the way back down to the E7.
The rest of the song just rocks back and forth between A7 and E7, and both chords are on the same fret. It's a simple matter of sliding 2, 3, and 4 up and down the frets to the right places and keeping your index finger in place.
All of these changes are perfectly acceptable and don't need to be changed from what I can see.My only advice is to play through slowly, concentrating on the chord changes, not the chords themselves.
