Spacklehead

I'm not quite sure what you mean by going back for your RN or BSN. Do you mean going back to a diploma program to prepare you to sit for the NCLEX when you say "getting my RN?" All three types of programs (diploma, ADN, BSN) will prepare you to sit for the NCLEX-RN exam. You only get your "RN" when you pass the NCLEX.
I do know that some hospitals in NJ will only hire BSN's (Hackensack comes to mind, unless this has changed over the years since I've lived in NJ). I don't believe there is really much difference in salary at hospitals that hire all three types of grads (diploma, ADN, BSN), so that really isn't an issue. As far as other nursing jobs outside of the hospital arena, community health agencies usually only hire BSN's, pharma companies hire BSN's, and public health agencies hire BSN's.
As far as good schools of nursing in NJ, I can only comment on BSN programs. The College of NJ and Rutgers are two that come to mind that have very good reputations when it comes to nursing programs.
To answer your third question, yes, most programs do accept students who have a bachelor's in another field. As far as the pre-reqs go, you would have to contact the program coordinators at the schools that interest you to get a definitive answer to that question.