The frame of the 531C Reynolds tubing is rusting, What is the most appropriate method to remove and prevent the rust? Would it be removing the rust and repainting? If so could you like me to resources to understand step by step?
That would totally depend on your wishes for this bike. Also it looks like this isn't the only spot that has corroded. On the tube going to the rear axle there are also plenty of darker spots. They could be dirt, but might as well be rust.
If you want the bike to stay as original as possible I'd suggest to grind down the rust until shiny bare metal shows, and covering that with some good coats of clear paint. That way you can maintain the most of the original finish. You could alternatively try to find a paint in a matching color.
If you want the bike to be in the best shape possible it might be wise to completely strip the frame from all paint, and respray it completely. In this case you can use a chemical paintstripper to get rid of the current paintjob, and respray in a color of your liking.