Regular plaster needs 3-4 weeks to cure before priming and painting. Drywall doesn't need this time.

Use a PVA (Polyvinyl Acetate) wallboard primer. This type of primer is specifically designed to neutralize the high PH of these substrates and seal up the pores, ready for painting.

Generally these primers are inexpensive, when compared to other primers and paint but there is a wide range of manufactures with a range of quality. Choose a good primer, this is the foundation for everything else.