Don't go by accreditations. I had my son in a private school that had all sorts of recognition, awards, etc and then all heck broke loose. The principal was charged with all sorts of things (a laundry list of stuff) and the school was closed. It opened my eyes to the fact that no matter what they tout on their website, it may not be the best place.
Since then we went to a very small private school that has been amazing for my son. I would suggest 1) go to the campus and see everyone in action 2) ask if you could speak to a few other parents of children that would be in your childs grade (normally they'll have a few parents that are willing to tell other parents about their experiences) 3) Look on yelp, greatschools, etc 4) If they pressure you to make a decisioin, run the other way. 5) speak with the principal and ask for a copy of their handbook to look through before making any decisions.
Definitely ask about their view on parent involvement/volunteerism. Do they require parent volunteers? Some school differe grealy on this whole subject. Also, maybe take a look at their cirriculum and also ask what style of teaching they use.
Hope that helps a little. :)