Gina answered just as I would have. I would however suggest that you access the school reports that the state complies to see if an area that you are interested in is the right fit for your criteria. I have the links on my website. Hope this helps!
As a mom of 3 children myself I understand your concerns about moving to a good area. Unfortunately we cannot "steer" you one way or another. Only you can determine what area is good for you and your family. I may love an area and you may hate it and vice versa.
As far as the second part, if you are applying for a mortgage, yes, the bank will now your credit score, credit history, debt to income ratio and will know if you are putting money down or not. Your best bet is to speak with a loan officer to determine if you would even qualify for a mortgage at this time and if not, then they can at least go over your financials with you to try to improve your score and save some money for a down payment.