Zinsser do make excellent primers. A shellac based primer is advised to seal the wood so the grain doesn't show through the paint ( the oil in the grain will work it's way through the paint ).
Interestingly I painted a door a little while back with a paint I would not have recommended, Dulux Gloss White ( water based ) but actually it's done a really good job. Seems they have improved it recently.
I wouldn’t gloss anything as it is a bit old fashioned! I’ve been doing all the wood work in my new place with Johnstone’s trade eggshell first time I’ve used an oil based paint in years but it goes on beautifully and the finish is stunning. Definitely worth the smell and the brush cleaning hassle!