man such a difference between the areas where the finish came off and where it stayed on.
the ultimate way to do it would be to get the whole thing sandblasted back to a uniform finish and go from there
but you could just sand it off too (a dremel style rotary tool would be useful for the welds, and tricky reach bits)
id think that as long as the bare metal isnt exposed, the oxidisation shouldnt get any worse. its pretty gnarly on that bb/cs junction though (looks like its been exposed to the elements for a while) but as long as you get it smooth and get most of the rust off, id imagine it should be fine once painted, especially if youre laying down some primer and lacquer too.
in the future, if the paint starts to peel back and expose the metal again, just spray over it again and it should be fine
also another possible option is to use vinegar to get rid of the rust. however i know very little about this technique other than people use it to clean rust off old chrome parts (especially old/mid school restorers). might be better than sanding, might not be-youd have to check some how tos etc