Welcome to lapidary!
You can purchase rubber burs, polishing wheels and rods from the likes of Otto Frei, Cooksongold, HarbourFreight and many other suppliers. Some come pre-charged, with the polishing medium in the rubber and you will have to charge others, such as felt wheels, bonnets or pads with compounds that have various "grit" or "mesh", with higher numbers indicating a higher degree of polish. To achieve a high level of polish you will need to go through the grades, that is, use one grade of polish to completely remove any lines from the previous grade. Skipping grades can be done at the risk of ending up with a collection of finely polished scratches, which appears to be the effect you are looking to achieve.
Polishing compounds are often proprietary, but combine an abrasive such as silicon carbide, carborundum, emery, pumice or diamond in a binding agents or matrix such as wax and oil. Different grades are often provided as different colours to distinguish which is which and so you will soon learn which colour to use next (within the same proprietary range).
Different materials may be used in the final polishes, such as Tin Oxide, Cerium Oxide or Diamond frequently achieve good polish on some materials, better than others. Finally, no doubt polishing is probably a science but there are different theories about what it is and achieving the ultimate polish, whilst science may underlie it, is definitely an art.