I would use one transformer, fused in the primary winding. If the ~15V secondary does not have a center-tap, then use one 5A 100V full-wave bridge rectifier, and one big ~10,000uF 25V electrolytic filter capacitor. Wire the 7812 and 7815 as shown on the data sheets. Feed the 7805 input from the 15V output, to minimize dissipation in the 7805. Mount all three regulators on a large finned heat sink, you will need the mica washer insulating kits.
If you can find a transformer with a secondary center-tap, then everything as above, except feed the 7805 with a second large filter capacitor from the center-tap. A second rectifier is not required. That way, less heat will be produced in the 7805.