For mild surface rust, simply apply by brush or spray bottle some form of phosphoric acid. Let it dry, and spray with rattle can primer or paint. Problem solved.

You could also just apply the acid and not paint it. Problem solved. The paint is just extra insurance in case the metal gets wet in the future, which could happen from condensation.

Of course, it's better to physically remove rust residues with sanding or wire brushing before applying the acid, but if this isn't done, the acid will still do a good job of killing the rust, especially mild surface rust. If brushing it on, use a nylon bristle brush or the bristles will be consumed. The reason it is better to physically remove the rust first is that the acid strength is depleted faster when rust residue is present. If the residues are not physically removed, apply additional coats of acid. Where the residue is well removed, usually only one coat of acid is needed.

Search You Tube with "removing rust with phosphoric acid " for several videos.

Many restoration shops and many collision shops use some form of phosphoric acid on all bare metal before primer, and most automotive paint stores sell it. It is a well known and common treatment in industrial applications for metal before primer, sometimes called "bonderizing". Rust Mort contains 40-60% phosphoric acid according to their safety data sheet. Other common brand names for phosphoric acid are Ospho, Rust Cure, and Gem Rust Killer, available here. Some retailers may have Gem in smaller containers than 1 gallon.

I've been using Rust Cure phosphoric acid for many decades, including today. For unseen areas like the underside of a car roof, I would apply the acid and allow it to dry. For visible areas, the acid should not be allowed to dry, as it will leave a crusty film. In this case, I allow the acid 15-30 minutes to do its job, wipe off with a rag, brush on paint thinner, wipe off, then paint after the thinner has dried. Do not rinse with water - paint thinner is better. To remove the film after the acid has dried, re-wet with acid and rinse with thinner. Never apply phosphoric acid to any zinc plated item as it is very reactive with zinc and will ruin any zinc coating. Phosphoric acid will cause discoloration to painted surfaces or epoxy-coated shop floors. Phosphoric acid will ruin your clothes. Wear nitrile gloves.

Once upon a time, after a plumber had used a metal snake in a commode, there were numerous, unsightly, dark metal markings on the bowl surface. I poured in some Rust Cure, and the bowl became spotless.

Rust Cure, Gem, and other similar forms of phosphoric acid are typically green colored. Phosphoric acid is much safer to handle than hydrochloric, nitric, or sulfuric - getting it on your skin does pretty much nothing, but if it itches, just wash it off. Soft drinks contain phosphoric acid. But if applying with a spray bottle overhead, you certainly don't want to inhale it.