I recommend a brass wire brush and oil for cleaning rust off chrome. The more the bristles are flatten the better! The brass will not scratch the chrome and the oil, well that's just there because it makes it easy to wipe off the loosened rust so you can see your progress. Sure you could use steel wool but you run the risk of scratching the chrome if you press too hard. Others swear by Aluminium foil, but I have never seriously tried it - The brass brush was just so damned fast with its conveniently placed handle.
Good luck with the build.
Good luck with the build.