If you plan of a film finish I prefer to leave the bowl on the faceplate and do the sanding between coats on the lathe. It gets so much smoother that way. Anyway if you wish to use a water based polyurethane you probably should apply a 50/50 mixture of linseed oil and mineral spirits to enhance the grain. The water based poly otherwise looks bland to me. Then let dry overnight and apply a coat of zinsser sealcot and then start applying the poly. I wouldn't use an oil based poly for the bowl as it would turn yellow as it ages. An oil based poly is better for darker woods.
If you like lacquer I would just coat the bown with a vinyl sealer and then use a cab-acrylic lacquer as a topcoat. The nitrocellulose lacquer is the most common but it will yellow as it ages. The cab-acrylic will remain clear.
You could also finish with tung oil however it takes a very long time between coats to build a finish. The best way to tell when a coat of tung oil has dried enough for another coat is to briskly rub the finish with a clean cloth and see if any of the smell rubs off on the rag. When there is no smell then it is ready.
A lot of people like shellac however it works like lacquer and is better sprayed since it melts into previous coats.
If you want a really hard durable finish then you might want to use a conversion varnish. I've seen some that paint and varnish remover wouldn't touch.
