Re:
You'll probably want to strip away the paint on the lugs by the seat cluster to start with, since there seem
to be a few rust bubbles round there suggesting rust under the paint.
You can scrub off the loose rust with a wire brush (a brass wire brush is probably best).
Then there are several products you can try: oxalic acid is supposed to neutralise rust; naval jelly or rust remover (I think this is actually just oxalic acid suspended in a gel); or rust converter (e.g. Hammerite Kurust).
Most of those should be easy to find in a DIY or car repair shop. I once soaked an entire fork in coca cola to get rid of surface rust on the chrome. Worked OK but I wouldn't want to do it again.
After that you ould try putting primer on the metal before you paint. Again, car shops sell smal retouch paints
including primer. These work quite well. For the actual paint, it might be worth trying nail polish. It dries harder
than retouch paints and there are A LOT of colours. I got a pretty much perfect match with nail polish for one bike I did up.
Cheers,
Johnny