Tom, I notice that you have been focused on the Briggs and Stratton engine in your plans. Unless they have been abused or neglected, those engines are usually quite easy (and inexpensive) to get running well. The remainder of the mower is likely to take considerably more time and money to get into good working condition. You may find it easiest to plan for this project to proceed in stages, probably with assessing and diagnosing the engine's needs as the first stage. With that behind you, you will be better prepared to work on the mower itself.
Because you have an early (one-piece deck) SB45, the machine is potentially a collector's piece, which is worth dealing with carefully one step at a time.
