Welcome to the area. There are both private and public schools available in the area, but unless your children have special needs, I think you'll find that the public school system is excellent. It is ranked as one of the top ten public school systems in the country.
As Stan said below, one of the first things you want to do, is to select a Realtor to guide you through the process. I would recommend that you interview a couple of Realtors to see who you feel most comfortable with. I grew up in the NYC area, but have been down here now for over 30 years, all in the area that you're looking to settle in. There parks and the sports facilities here are excellent, so I think you'll be able to find exactly what you're looking for.
I would love to interview for the position of your Realtor. My contact information is below, and I would love to hear from you.
Keller Williams Realty
(703) 599-4755 - cell