Siding a sun room with 2 screened in walls and curious about siding details. (12×20)

I have BlueSkin house wrap and planning to put primed pine ship lap siding.

The room should not see rain and the screens prevent most of the water during rainy windy days.

Should I put some kind of rain screen product or furring strips on top of the house wrap?

Also thoughts on 16 gauge stainless 2 1/2 inch nails on the face to hold it? Solid sheathing with stubs.

Located in the Northeast and not close to water.

Thanks for taking a look!