How to choose chord shapes for smoothest transitions

Focus on hitting the tones that make them up first and think of holding the chord shape as completely secondary.

Play the 1st chord, and then search for any similarities in fingering as well as overlapping notes or the nearness of notes between that chord and the next one. Sometimes a trick you can do is "pre-fret" part of the next chord so you have fingers there already (people do this to Zepp's Rock and Roll when they bounce between the A and D chords during "Been a long time..." as well as the famous riff in Cats in the Cradle).

If you are an acoustic soloist, well then you are a 1-man-band and you need to get good at smooth transitions. But I don't worry about bottom E string notes when there are bass players/keyboardists around. Also if you are in a band, that G6/E and C6/A you have there would be a straight G6 and C6 for me because the bass would play the E and A and it would even sound better that way since I wouldn't combine frequencies with them.

Check the tabs on songs out there you know that have bright acoustic chords in them. You'll see in many cases the chord is not a 'standard shape' at all and the guitarist is simply hitting the 'right tones' for that riff/phrase. A good example of this is to look at the tabs (NOT chords) to the Rolling Stone's Angie. The Em7 and C chords in the song have shapes you won't find anywhere. At best, they are 'abbreviated' and contain only the essential triad, done so for the sake of fluidity. Eliminate doubled notes in all shapes if it makes them easier to transition to the next chord.

Well, I hope that helps.