I have fresh drywall and bought some PVA primer. We plan to paint with semi-gloss so that the walls can actually be cleaned.
Per KILZ PVA
Designed for use under flat and low sheen paints only. Do not topcoat with glossy paint finishes.
I'm aware that you cannot just paint over a glossy surface without proper preparation but I wasn't aware of any restrictions for primer+sheen combinations.