I would definitely make the stringers out of pressure treated 2x12. Wide treads could require too deep a notch, even in a 2x12. You would need to lay it out and see. 8 inch rise is more than allowed by code, at least for indoor stairs. You want to keep it closer to 7 inches. 12 inch tread is fine IMHO. Normal treads come 12 inches wide if I remember right. My last stair build was indoor, however, which is what I remember.
You are right that PT straight from the lumber yard will not accept paint well but if you build the stairs and then come back in a month, it will. (Maybe 2 months if there is a lot of rain). And the time with no finish will not hurt the PT. I probably would not paint the treads since whatever you use will wear off. I would not use any fancy joints, especially in wet PT they won't work great and will greatly add to the effort. Simple PT stringers and treads with screws to hold the treads down will work well and last a very long time. If necessary, the screws can be retightened after the wood dries some. This is carpentry, not even finish carpentry, work but stairs built this way hold up and last. You could be dressier with the posts and rails. I recently used composite vinyl material on my dock and it was not difficult to work with. The big advantage is no painting. It can be used for handrail with different connectors. PT stringers and treads with vinyl handrails and ballisters would look pretty good, not require much maintenance, and last a very long time.