Cheap metal that can polished to look like chrome plating??

Aluminum. iirc, aluminum is used for the mirror in reflector-type telescopes.

Various non-stainless steels can be polished so that they look chromed, as well. Interestingly, this effect can be achieved by just prolonged tumbling in the right media, + a little finish polishing. When tumbled to this degree, non-SS steels are also surprisingly resistant to oxidation, altho not quite like SS.

And of course, SS (both magnetic and non-magnetic) can be readily polished, and in fact is used in some mirror applications. The military used to issue approx. 4x6 hand mirrors made from approx. 16 ga SS.

Non-SS polished metals, incl. alum, should be coated, tho, as the shine won't last long without some kind of laquer et al.

The people on rec.crafts.metalworking should have more to say on this.

Here is a link to a thread in practicalmachinist.com

The late Frank Sperl had some very excellent advise about polishing aluminum. This link will get you started. He tumbled it in walnut shells, and had an entire recipe. Find out all you can from him.