An APU on a 737/A320 will burn about 100kg an hour - roughly $90 at current fuel price. A 747 will burn 1000kg an hour. As to where APUs will be used, it may be the airport demands APUs can only be used in the 20 minutes prior to departure for environmental reasons. That's when you discover the airport charges a lot for the use of ground power! But that is the crux. In our operation, we tend to use ground power / air con at our home base because we have negotiated a good deal with the airport. At nearly all our airports we use the APU because it's cheaper.
Captains usuallly do the PA because (so we're told) the passengers want to hear the Captains voice for reassurance. First officers often do the outbound leg because the Captain usually gives them the choice of sector, and most chose not to fly into the home base so they get experience of all the outports. But some they can't fly to. Sometimes the company operations manual will limit the weather conditions First Officers can operate in - for example, 20 knots cross wind is a typical limit. And also some airports are more difficult.
Airports are usually categorised Cat A,B or C. A means few difficulties, B means some difficulties and C means significant dificulties. Cat C airports are invariably Captain only operating. We have two Cat C airports on our network. Kathmandhu in Nepal (a very steep non precision approach over terrain) and Busan in Korea (a very tight and difficult circling approach). Both are Captains only, partly for difficulty, but also becuase special simulator training is required for these airfields and it's cheaper to train just half your pilots to do the handling.