Ultra-novice wood turner here. Do you need anything special to

high gloss polyurethane?

>>1001690
Took me a lot of sawdust to get this trick right.
Superglue.
Sand down to 1000 grit, burnish with sawdust if you are inclined then take a paper towel and fold it as a pad then apply liquid not gel cyano to the piece at medium rpm and spread it smooth. You have to be careful about it hardening from heat while the towel is on it or you'll get paper bits.
I implore you to give this a go, it's cheap and gives good results with a bit of practice.

>>1001690
Wood buttplugs...

If you are as new as you make yourself sound I'll ask the most basic question: are you polishing the thing on your lathe properly? Using several grits of sandpaper (120, 240, 400, 600, 800, 1200) before using any bees wax or oil or whatever?
Are you using a wood that polishes well?

>>1001690
2 coats shellac or polyurethane should do the trick. The problem is you have to seal the wood first. Also consider the rpms on your lathe. Is it spinning so fast that it's throwing the coating off?

Shellac gives it more of a warmer yellowish tinge and is natural and less toxic, it's also time tested. There are multiple types of polyurethane and it's easier to remove and work with because you can thin it with mineral spirits, Naphtha etc..

Apply 1 coat and thin polyurethane with said spirit (Naphtha shortens drying time with also means work time) if desired. Sand light enough to take the gloss off with 800/1000 grit after the first coat CURES, or take a rag lightly damped with mineral spirits and go over the surface to de-gloss it. Do not sand or do anything until after the CURE time not until it's "dry to the touch", also never apply any paint or adhesive to a glossy surface or an absolutely dust free surface (yes you have to wipe it down each and every coat).

If your using polyurathane on the last coat, try spraying it lightly with the canned stuff, without it on your lathe. If you're using shellac, you're gonna have to wet sand or polish it to a shine.