Progression of side pull brake service on vintage bikes.
I just want to stop-
Replace rock hard old pads and cables.

I want to stop better-
Above plus using Kool Stop pads, aero levers, clean rim braking surface with Alcohol etc.

I really want to stop.
Above plus replace calipers with modern dual pivot brakes whether factory or aftermarket like Tektro.

Centering Side pulls
Dave Moulton's Blog - Dave Moulton's Bike Blog - Centering side-pull brakes