I may not be 100% correct, and I'm sure someone else will chime in if I mess it up, but I believe that First Pilot, Copilot, and AC would all count towards your total time.
In regards to PIC, most airlines want to see PIC in terms of signing for the aircraft, which would just be AC time. "At the controls" PIC time is anytime you are rated to fly the aircraft and are sole manipulator of the controls, so I believe that the time before being qualified as AC can be logged as "at the controls" since you were rated to fly that aircraft.