Plan the port transfer separately from your walk around the old town.
A walking day in the old town: follow La Rambla into the Gothic Quarter, with its narrow streets and squares, and explore around the cathedral and Plaça Sant Jaume. Give yourself separate time for getting back to Moll Barcelona; it isn't part of the walk.
Sagrada Família: book an official ticket, make the basilica your main visit, and leave room for the journey back. Worth knowing: the UNESCO listing covers Gaudí's Nativity façade and crypt, not the whole basilica.