Cleaning Rusty Metal Shelves?

I've bought some antique, not valuable but great looking, metal shelves that are quite rusty. The shelves were originally red and I'd like to keep them in their original condition, but just tidy them up a bit.

I don't mind if some of the rust stays. They look like they need some rust removed and then some sort of shining product. I don't know if this possibility exists! Any advice would be very gratefully received.

By Kate D