I'm pretty sure (barring injury or a trade) we won't see Weiters. I also don't see Gamel coming up unless someone gets hurt. LaPorta is intriguing, but the Olympics may affect his schedule.
Price is the overwhelming favorite to me. After that I look OF, with McCutchen, Snyder and Rasmus all possibly seeing some time (look at Rasmus first, especially with all the health issues that OF has had). Then either of the Oakland pitchers, Cahill or Anderson, or Chris Tillman, who has pitched his way into elite prospect status.
I have to ask, your dynasty league doesn't allow for minor leaguers to be picked up? I thought that was one of the big selling points of a dynasty, being able to invest in a guy for the long term before he is a star.