Accredidation

This may seem like a silly question to many of you, but I'm new to nursing. After doing some shadowing and research on the profession, I believe I want to become an RN and maybe eventually do advanced practice. Although my grades make me competitve for admission to accelerated second degree BSN programs, I want to have one or two backup schools that are less competitive than the state schools I'll be applying to. When looking at smaller, private schools that offer BSNs, but not necessarily accelerated programs (like Resurrection University in Oak Park, IL) I'm a bit confused about the accreditation. What is the most important organization to accredit a nursing program since I've seen few different acronyms out there?