Are you using acrylics?
If so, are you using a compressor or a can of air?
If a can of air, there's your problem - the propellant can be oily.
else, the surface of the model is oily.
If you're using enamels, and a compressor, then you should check the water trap (or you should have a water trap on the compressor).
I paint with acrylics, because it's easier to undo my inevitable mistakes with denatured alcohol (methylated spirits).
My main acrylic paint is Vallejo; their paints cover well and are relatively inexpensive. The downside is that they're delicate, even after they're dry. Vallejo makes several polyurethane primers, but they can be finicky. Other acrylics that I use are Tamiya and Testor's Acryl.
The best primers I've found so far (as good or better than the gold standard, Mr. Durfacer) are the
Badger Stynylrez primers. They're acrylic, but dry quickly and produce a flat, hard surface that conforms to fine details. Acrylic paints stick to it well.