So I'm considering rebuilding my 1970 Raleigh Sport that has just been sitting in the shed in parts. The only major concern is that the fenders have pretty serious rust along the edges. Initially I was going to strip the frame, fenders and chainguard for a repaint but my partner decided she likes the original color (which suits me just fine--I'm not confident in my painting skills).

What is the best way to keep the rust from growing? Should I leave the rust as it is? The rust has completely eaten away at the edges of the fenders.

Along the same lines, what is the best process to remove the surface corrosion from the rims, spokes and handlebars?