My background is retail paint store management 21 years.

You need to use an oil based primer like Zinsser's Cover Stain, Insl-X Prime Lock. This will block the chemicals used in the pressure treatment from bleeding through the paint film. Acrylic water based primers "might" block these chemicals, oil based "will" block these chemicals.

Then you can use an acrylic water based stain, acrylic water based house paint. I suggest acrylic because oil based finish (final coat) products have a tendency to mildew, they also have a tendency to chalk quicker than acrylics.

Benjamin Moore's Arborcoat acrylic solid stain line (#640) is a good one. Or, if you want even more longevity, go with Benjamin Moore's Aura line. (#629)