I agree with everything that's posted. Also, rely on YOU - if after all your research and questions, something seems "off", follow that instinct.
For me, I found a huge difference in "For profit" vs "not for Profit" preschools, usually YMCA, Park Districts, and Church are not for profit, this is not an "absolute' or a garuntee of course. I was a certified teacher, stopped working, got involved in Daycare, and Preschool (for me it was the hours the center was operating, if they served meals...) In one "For Profit" center, it was first established in a Jewish Community Center, and had a wonderful following, great word of mouth, they lost the lease, and opened in a 'strip mall' that wasnt in a high traffic area... the things that went on behind the scenes would curl your hair, and make you NEVER take a child to Daycare... (a 2 year old classroom of 15 kids one adult/teacher, not enough toys, an infant room that handle babies younger than 6 weeks, 2 adults (one being ME) and 16 babies - it was an amazing time, I learned and loved a lot that year, and I didnt know any better!! We fed the babies, changed the babies, moved the babies, all on strict schedules, we never sat and played with the babies tho!! I could go on... When the 'state' would come to inspect, you wouldnt believe the amount of adults and toys that would show up in that center!! All nice and legal.
Then I went to work at a Park District - boy what a world of difference, look at the "consumable supply" budget - paper, crafts, playdough... This Park District also went for National Accredation (the above link you provided, acronym is NAEYC - pronunced naycee) and let us as teachers work up and go to Institute days - I was a presenter, so I would ask how the center handles continueing education... do they encourage, or expect teachers to go to inservices - inservices provides ideas, and help for the teachers... I loved being a presenter, I did mine on Drama...
How do they handle discipline, what if your child is a "biter"? Again, remember they may tell you anything you want to hear to get your business, but what happens after you sign up? Know that you will pay for days you dont attend, sick days, and the 6 Federal Holidays (New Years, 4th of July, etc) and you may have a vacation policy... think of the overhead the school has to pay....
I've heard a lot of good things on Montessori, and I've heard some negative, it all depends on how the center operates imho!!
Good Luck!