I do quite a bit of painting and can't emphasize enough the importance of a good primer. On new indoor wood, I would probably go with Zinsser B I N. It's white, shellac based and will dry quickly.
For paint, though it's a very high dollar item, you just can't beat Sherwin-Williams Duration. I have used it a few times and love it. One coat will probably be enough.
A couple of things...
Scuff sand after the primer has dried and before the next coat of primer/paint.
Blow/vac/or tack off the surfaces before the next coat
The higher the sheen with paint, the better the durability.
Never lick a steak knife.