Accredited?

I plan to attend a private school to receive me Lpn this year and once working , i intend on going to school part time to get my BSN, and eventually my CRNA. I was curious if the school that I am attending would be fully accreditted for a CRNA program when I do have my BSN. Basically what I am trying to say, is should i go with a University or public school rather than a private school? Please help me someone! Thank you!