Originally Posted by David Newton

If you are planning on keeping the bike for the long term, go ahead and scrape the paint off the rusted areas and dip the entire frame in oxalic or phosphoric acid to kill the rust inside and out. Then do your paint touch-ups. There are endless threads on OA treatment here in this forum, do a quick search.
If riding is going to be a flash in the pan, just scrape the rusty spots and touch-up.