I'd avoid a private school for online. The point of a private school, undergrad, grad, or post grad, is to get you connections - not just the socially constructed prestige. The school will literally (or they should if they're going to call themselves 'worth the extra $30k a year') hook you up with many professional networking opportunities, connections, and so on. Online though? What that means is you aren't developing any face to face relationships with any of your instructors. You're a nobody after you graduate. It defeats the entire purpose of spending all that extra cash.
Go public if you must do online. Hope it's accredited and looked highly upon in your specific field. Avoid papermill schools I.e. you will never in a million years get hired as a state licensed therapist in my state with a DeVry masters degree, all the practices and schools here will think you're a fucking moron and equate you to another undergrad.