Agreed, a PA would cover all of the roles you are interested in! The nice thing about the PA is that it's pretty broad in scope - kind of like the BSN is. You go to clinicals in a variety of settings and come out as a type of generalist able to work anywhere. The ER and primary care are similar in a lot of ways, so you could easily bounce from one to the other IMO.
The good thing about the NP is that most NPs are experienced nurses who have a good idea what they want to do. If you were a nurse already, I'd tell you to go the FNP route.
I'd go with whichever program is cheaper! LOL - where I live, the NP is about $15-20K and the PA is $150k, not the other way around!