When I do a refinish on anything I mess with,(guitars, or ukes), I finish them in nitrocellulose Lacquer. It is a bit more costly than just a more modern poly coat, but, you can get a beautiful finish with it. It was more commonly used years ago, and many of the top tier guitar manufactures still use it. If ya take the time to sand between coats, and polish it, you can get a very glossy, glass like finish with it. I didn't do all that with this uke. I simply applied about 6 coats of Nitro lacquer, but didn't polish it. It has a natural shine to it without polishing it, but if you polish it, that is when you get the very glossy glass finish. I may do that with this one sooner or later, but I just wanted to get it back playing for now. I'm loving it, so I may go ahead and put a couple more coats on it, level & polish it. With the wood on the front, this if I do that will REALLY pop.
I sanded all the original poly "statin" finish off with a 100 grit paper, then 300 grit, and finished with a 400 grit, as well as the dark edge burst the builder put on it, wiped it down with denatured alcohol colored with a reddish mahogany toned pigment powder to bring the grain out with some contrast, then 4-6 coats of the Nitro Lacquer. Actually, I did a pretty quick job of it. If I were finishing it for a re-sale, I would have gone on up to about 800 grit, then 1000-1800 grit between Nitro coats, then final polish. Still might end up doing that after I play it for awhile tho.
I did my Gibson Les Paul that way, and you can see your face and shave in it's finish.
As far as materials, I use "Reranch" products. They are not the cheapest in cost, but I find are the best out there. Also makes it much easier to work with if you heat the lacquer before you shoot it. I heat the materials to between 80-90 degrees, and also heat the surface I am shooting a bit with a hair dryer. It really lays on very smooth and even if it is heated a bit. Actually, some know when I was able, I used to restore classic cars, and hot rods. Always did my own body work, welding, and painting of my hot rods, and the techniques I used on that, are very similar to refinishing an instrument.