Mike - You’re making me blush.🙂 And tbh, I’ve never been totally happy with my polishing. More haze than I’d like.
But to answer the original question. First, I don’t think you want to polish it by hand. If nothing else, get a HF random orbit sander, and get a polishing pad for it.
The first few times I polished, I used Mother’s with a Porter Cable random orbit polisher. I used pads from Auto Zone, and just used pressure to keep the pad in place. Not ideal, but it worked.
After the first few years of that (I do an annual polish, usually for an auto show that runs each year), I started using Nuvite with a Cyclo polisher. Nuvite comes in a range of grades. If you have heavy oxidation or scratches, they recommend you start with a compounding/coarse grade, which you apply with a circular polisher - which essentially means a drill with the right pad attachments.
You’ll have scratches after the compounding, but they all come out when you use the finish grade.
I still use Mother’s here and there, and I think you can get a very good shine with it. Probably a good place to start, and decide how much effort you want to put into the polishing. I end up removing my fenders and windscreen, exhaust, etc, before I polish. But it’s obviously not necessary to go that far.
Oh, and regardless of what you use and how you polish, wear neoprene gloves or your hands will be black.
Enjoy! 🙂