The barre chord you called up, I ususally form with my index for the 5th fret barre, with my pinky barring the three strings on the 7th fret. The 'X' is accommodated by selectively not strumming the 6th string. But that's only because my ring finger refuses to do the job that my pinky performs without complaint. There is no one 'right' way for a lot of the stuff we play.

I had a friend who barred the first three strings with his index finger for any D chord formation, because he had broken his middle finger at a crucial point in the development of his style. You work with what you have.

I finger the G chord based on what I will have to do next. I try to free up fingers to form the next chord before I actually need it. This allows smooth transitions, and to me, 'smooth' is the goal.