Personally, I only know of two different accreditations for RN programs, NLNAC (accredits all kinds of schools from associates degree all the way up to masters programs) and CCNE, which is usually just for BSN/BAN and masters programs. That's really the only difference.

Yes, it's important to go to an accredited school, or you won't be eligible for licensure.

But you should know that once you start a nursing program, it is really difficult to switch to another school midway through a program. If you're just taking your general ed courses it isn't a problem, but nursing courses themselves almost never transfer equally, and you will probably have to start the entire nursing core over at the new school. Since every school runs their programs differently, courses don't match in content. Also, since nursing school admission is so competative, the schools have a hard time accomodating people trying to transfer in mid-way. There aren't spots available. They need you to start from the beginning.

I'm not saying it's impossible, but it's going to take you a lot of research and phone calls to find a school that would transfer in nursing courses and allow you to jump into an existing core.

Good luck!