welcome to the board!!!! I'm Emma (28), Mummy to Gaby (5) and Emmy (22mo).
I don't think there is anything wrong with starting your stash before your baby is born - I did it, and I am glad I did! As for how many and how many of what? I have an enormous collection of all the different types of diapers... I have over 150 diapers all up, and that is rather excessive
The most basic, cheapest stash (made of AIO or pockets) you could probably have would be 2-3 dozen Sunbaby pocket diapers - they are really cheap, but seem to be pretty good quality
I do recommend buying newborn size diapers for the newborn stage - and to be honest, if I was going to be buying newborn size diapers, I would buy the whole stash preloved - because they are in them for such a short amount of time....