I used sandpaper that I got from the auto parts store. I worked my way up from 180 grit to 320, 600, 2000 (wet sanding), and finally 3000. I would probably include a 1000 grit in there as well.

I rinsed the metal with soap water before using a polish kit that I ordered from Amazon for ~$35 (came with several cotton wheels and the compounds) I attached the wheels to a hand drill. Used the brown then white compound.

If you search “Bikeit UK polish” on Youtube, you’ll find video titled “How to clean and polish metal to a mirror finish” that I recommend watching.