We have plastic coated drywall and use the Zinsser brand Bulls Eye 1-2-3 primer for all surfaces. It works great! Once the primer is on, the paint (and spackle, should you ever need it) will stick to the primer just fine. The primer is a bit expensive, but well worth it. It even sticks to the metal strips we're putting on the corners.

Good luck!

I bought an older fixer upper. It had been fixed in the past and had wood laminate floors and a bathroom that was updated in the past and not a 1970s one.

The walls were not painted. The bedrooms had this odd wall covering that looked like corduroy fabric., That was not too hard to paint, but it was a dark beige and needed 4 separated coats.

The living room walls were panels that were a faux gray wood pattern. That was hard to paint because the roller just slipped off, but eventually I got the hang of it and the cheap white flat paint worked well after many coats. It now looks like dryway.

The are probably VOC panels (vinyl-covered-gyp). Yes that can be painted or finished in several different ways. I'm going to recommend a site that covers this topic better then me, just wish to recommend Kilz as the best primer one can use. (Personal experience).

Here is a link that might be useful: Updating VOC walls in Mfg Hsg