It sounds like these walls are very well prepped for painting. Wallpaper adhesive has been stripped, washed and double rinsed; and the walls were sanded and texture applied. I see no problems here. In fact, most quality interior paint is self-priming, and a separate primer may not be needed. I recommend you go to a professional paint store, take their suggestions for high quality interior paint and application products. You can’t really go wrong.
A 100% acrylic primer would be appropriate and easy to use. Examples: Benjamin Moore Acrylic All Purpose 023 primer or Super Spec 253; Kelley Moore 971 Acryl Prime. If you prime, ask for primer to be pre-tinted towards finish color.