I use some stuff that reacts with any rust and turns it to black iron sulfide, which is inert. Rust actually catylizes more rust formation.
Rust Oleum makes a version of it called Rust Reformer. You can probably buy it at Lowes and Home Depot or maybe any paint store. It's not a paint but a chemical that reacts with the rust.
I coated my snow plow with it, and any rust was turned black and shiney parts just stayed shiney.
NAPA has a product that does the same thing. There are/have been 3 or 4 differents brands of this same chemical.
You can paint over it, if you want.
Ralph