Alright...we're speaking the same language.

You should be able to work by hand - if the plating is damaged enough to require machine polishing, it's probably worth considering having the item blasted and re-dipped.
My recent favorites are Meguiar's #105 & #205. Both work great by hand - especially so on chrome - and #205 finishes beautifully. My go-to sealant for durability is Four Star UPP. Two coats with 24 hours curing time in-between, and the chrome will be protected for at least a year.
For the clear on bodies I tend to start with Meg's Scratch-X. It's very gentle, and is designed to be used by hand. It breaks down very cleanly, and is very effective on light scratches and swirling. You can certainly get more aggressive if needed, but then it definitely becomes a case-by-case thing. For instruments in need of more work I also like Menzerna polishes, mostly because they utilize the same size of micro-abrasives throughout their product line. Makes it very easy to gauge the effort required, and even easier to jewel down to a perfect finish.
Speaking to your drill - if you want to go this route - Craftsman (and others, I'm sure) offer jeweler's rouge kits that can do some wonderful things to correct mild etching (i.e. sweat stains) in metal finishes. You have to be careful on chrome/nickel, as plating is a different animal than, say, polished stainless or aluminum, but the results can be stunning. I'd probably save this as a last-ditch effort...basically if you're pretty much resigned to having the item replated, and otherwise couldn't make things any worse.
I hope that helps. I don't want to bore you to tears or go off on a tangent, but I could talk detailing all day.
