Polishing a Micro Seiki RT 3000G Gunmetal platter

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.

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

Well, the OP didn't say what condition the platter is in, so it's hard to know what it needs.  What you recommended is on point if the platter is a little more worn than just lightly oxidized.