It would seem to me only logical that the home team would opt for the first base dugout. If only for the reason that if a player makes an out (except strike out), he is always in the vicinity of first base. That would enable him to clear the field faster and also get into the dugout for a rest after a tiring trot to first…
The Padres, and other teams, have reversed the sides of their bullpens and dugouts so the coaches in the dugout can see the bullpen and check out how someone is warming up.