I like to keep my old bikes as original as possible. And, I'm lazy. And, I'm cheap. So, here is the lazy, cheap solution:

I rub the rusty areas with heavy-duty paper towels, to get the loose rust off. Then, rub some more to get off any loose or flaking paint. Then I rub the rust areas with a paper towel dampened with rubbing alcohol to get off grease and oil. Then, I touch up the rust area with clear nail polish.

Using this method, I have not had any rust spots get larger or worse. And, the clear nail polish is not as obvious as my misguided attempts to cover the rust with either paint or nail polish that seemed to match the original color.

Why don't I use steel wool or something to get down to "bright" steel? On my bikes, the typical rust area is the size of a dime, or smaller. If I tried to get down to bright metal, I would end up removing some of the "good" paint around the rusty area, and making the damaged area larger.

Second, after I rub off the loose rust, I look at the surface closely. Usually, it appears that I'm looking at primer, or the "bonded" coating that most bike companies were using on steel tubes in the 80's and 90's. The rust I've removed is surface rust that did not penetrate into the steel tube.

Removing the protective primer or bonded rust-proof coating from a steel tube so that "bright" steel is exposed is more likely to allow "deep" rusting and pitting than if you remove only the surface rust, and put a air-tight sealer over the primer. (At least, that is what a lazy guy tells himself to justify doing this the lazy way).