How do you arrange your finger when changing from D to D7 and back? For D7, I thought about putting the index finger on the second string first fret and ring and middle on third and first string second fret, respectively. I could then change to D by releasing the index finger and putting the pinky on the second string third fret.
It'd be more comfortable to put middle on third and ring on first, which is maybe what you meant. There's really no need to take off the index from the second string, as the new D chord covers it anyway. With 12, yes 12 different ways to play that D,, you just need to try each one till you find the best to move from that to another chord. You may well find that you need a different shape to go to another chord comfortably and quickly, or to get to D from a different chord. Good luck, and remember, your hands and fingers are unique to you - just because someone else says his way is best, all it means is, it's best for him. (Or he hasn't found a better one, yet ).
This is always how I do them - I don't do it differently based on where to go to next chord. The best is to stick to one grip for one chord. Although in this case, it cause all the fingers to move as opposed to just shift the one string that is different.
The good thing about this is that you don't have to think about how to make transitions, you just let muscle memory handle the grip the instant you see a new chord, no matter where you come from in the previous chord.
That said, if this feels awkward for you, and you find other methods that are more natural for you, it is really nothing wrong with developing your own personal style. Everyone does not have the same hands, and there might be physical differences that makes one technique better than other for each person.