I'm sure there are bunches of various sanding and polishing pastes and liquids that are both commercially available as well as those homemade recipes. I have only used a few of them so I am far from an expert on any of this; however, I can explain those that I have used.
Some of the best polishing compound that I have used so far is
Stadium Pen Blanks, Magic Juice Polishing Compound. It comes in six grits. After coarse sanding, I apply a single drop to a small paper towel square, rub it on the blank to coat with the lathe off, then turn the lathe on to about 3000 RPM and use the same paper towel square until it has essentially dried and buffed off. Proceed through the grits. The blank turns out ultra-glossy.
The pitfall I have with all liquid polishes is that any pinhole dimple or other tiny pore will catch the polish and will leave a white spot where the polish dries in the hole. And the spots seem virtually impossible to clean out.
Personally, my best success rate has been by wet sanding with MicroMesh pads. Sometimes followed by buffing on a buffing wheel, but not very often. I do add about two drops of a wetting agent to my water for sanding. In my photography days it would have been a Kodak product called Photo-Flo, a combination of anionic and nonionic surfactants designed to dewet and prevent water spots on film. But at least for now I use Cascade Platinum Rinse Aid made for the dishwasher. Cascade is a nonionic surfactant which is a little less effective but is also less likely to form a soap scum in our hard water. Personally, I think the Cascade really helps extend the life of my MicroMesh pads by acting as a sanding lubricant.
For most non-CA finishes I use
Doctor's Woodshop. I use
Pen's Plus (DOC-108), but first I wet sand with paper using
Walnut Oil (DOC-106) as a sanding lubricant, followed by the Pen's Plus and sometimes a top coat of Doctor's Woodshop
Microcrystal Finish wax (DOC-110). Something I learned from YouTube videos of
Mike Meredith, the Doctor from Doctor's Woodshop LLC.
Dave