Polishing a Micro Seiki RT 3000G Gunmetal platter

Guys, I think what @horsestuff has in mind is removing the tarnish from the metal, like polishing silver.

There are hundreds of metal polishes out there. I personally like Menzerna Polishing Cream. It is a rub on, wipe off product, a cotton or microfiber cloth will do. You could use a random orbital polisher, but on something as small as a platter elbow grease will do fine.

As Carlsbad noted, work up to finer abrasives. I like the 3m foam sanding pads for auto use.   1200, 3000, 5000.    5000 makes a lacquer finish look like glass.  3m makes sandpaper and pads for polishing / fine sanding from 1000 on up. 1200, 1500, 2000, 2500, etc

I may have misinterpreted the question.  but looks like you're getting a variety of anwers.  Good luck. --Jerry

Would an orbital polishing tool be ok or is it better to use elbow grease?

Are you experienced with an orbital polisher?  If not, don't, in my opinion.