For a low buck approach, just sand, prime with Rustoleum red rust primer, and paint with some enamel - If you wanted to keep stones, etc from wearing the paint, then add some rubberized undercoat, or bed liner stuff, to that. But paint first, to get the rust fixed, if you want the undercoat to stick.
You can also kill the rust without harming the top chrome, by using an oxalic acid bath - This really works - I have done it.
https://bmxmuseum.com/forums/viewtopic.php?id=351132
You can also use citric acid:
https://bmxmuseum.com/forums/viewtopic.php?id=121049
If you remove rust from chrome with acid, you'll need to use a good wax on it at a minimum, and keep it out of the weather, or the rust will return.