"Picking away at" - I love it.
The paint looks like it's mostly intact and still shines. If it were mine, given that the places that are missing paint are so small, I would get touch-up paint (as close as I could get, slightly lighter than darker if an "exact match" isn't possible and run it. I had good luck at an large Advance Auto store. Or, for a bit more $, an automotive paint supplier (we have a large NAPA that has paint) can mix you up a touch-up color that will probably come very close (either brush on or a spray).
I'd also either do nothing except run a filter for the inside rust, or try Evap-O-Rust. I wouldn't coat it.
Best of luck with the bike!