You are probably going to have to paint those rims once you have removed the rust. I remember when I was a kid, the rims on my 'banana seat' bike started to get a little rust, and I cleaned them with steel wool...spotless. Oh my dissapointment a week later when they were rusted completely all the way around.
If you *really, really* want to make the rust stay away, use a product called POR-15 on the frame. You actually want to apply it with a little bit of surface rust on the frame, but once you put that stuff on, it seals whatever you stick it on, and it wont ever rust again. If you get it on your skin, you will have a birth mark that will not go away for many weeks...so wear gloves, and keep your hands away from your face if you are going to work with it.
