I know the material you are talking about; it is vinyl coated drywall, usually with a fine texture embssed in the vinyl.
I'm looking at the Zinsser primer application guide and they say any of their primers will work. I would use the Cover Stain (oil) if only because it is the cheapest. KILZ may have an equivalent but I have no experience with it.
Just before using the primer, wipe down with liquid deglosser to improve adhesion. The primer dries fast and can be painted over with either latex or oil enamel. For walls I recommend latex flat; it doesn't reflect and thereby tends to hide imperfections.
For more hints on painting, look at that topic on my website at www.bobf.info.