Apply your texture, prime and paint. The texture is going to absorb a lot of paint which is why it needs to be primed so the paint looks right.

agreed. To save time, when we roll walls we don't use a paint screens as much. We get the roller saturated and smear the paint around...then back roll. Using paint screens, takes longer as you can't get enough paint on the wall. This is messy so make sure you are taped and dropped. Unless there is an adhesion issue, we usually don't use primer. We just apply two top coats of body color.