It doesn't matter as long as it is not a for profit, private school. I would stay away from those. Overall, very few people will care although you do hear about how they don't like ITT Tech, Kaplan, etc.
As for ACEN accreditation, yes, no, kind of. Usually the schools
that do not have ACEN accreditation do have a transfer agreement in place for you to continue on with a BSN at a CCNE accredited school. Very few schools care about the ACEN accreditation if it is in the same state. When it is out of state they tend to become more picky. Like my school lost ACEN accreditation but managed to get it back. No one had any issues continuing on with a BSN. They managed to get it back before I graduated.
I have only seen one hospital system require an ACEN/CCNE accredited program besides the government. It was about three years ago.