Yeah definitely make sure your RN-BSN program is accredited and approved by the BRN BEFORE signing up for it. I've heard too many stories on here of programs lying to students just to get your money.
Also, it is true that it does not matter where
you get your BSN from; however, if you go to a more well-known school, future employers will choose you over another candidate with the exact same qualifications/ transcripts/ letters of rec, because they know the reputation of the other school.
I went to a small school with a fairly new nursing program. When I go to tell recruiters where I went, the have never heard of it and are weary of a school they don't know about. I know two major hospitals in my area only higher from the big name schools
.. and some postings even say, only to apply if you've gone to one of the particular schools in the area.
But at the end of the day, a BSN from anywhere is better than an ADN in most hospitals. Good luck to you!