You'd actually probably be quite surprised by the results you get with just WD-40 and some paper towels.
If that doesn't cut it, you can try soapy steel wool... but for that you need to use water so be extra careful.
If all else fails, you can go to the hardware store/auto supply store and get something called Naval Jelly. It's a rust dissolver that is quite strong. Cool thing is you apply it where you need it with a brush.
And for cleaning other surfaces, you can try a melamine sponge (Magic eraser).
There's also very fine grit wet/dry sandpaper...
If the WD40 soaked rag doesnt work, instead of water try using wd40 or a light oil like 3-in-1 with very fine wire wool, works well to remove rust stains.
Naval jelly is an acid based rust disolver which works well but the trouble is you have to wash it off afterwards.
A converter like kurrust is probably better for this as it converts the rust and gives a black primed finish, no need to rinse.
(too many years sowning rusty old cars!)
But once you've removed the surface rust, as long as you don't keep it in damp conditions again the rust probably won't be a significant problem again
