Staying on Disney property is a much better experience as you can use their shuttles to the parks, send purchased merchandise from the parks directly back to your room and also use the bus to and from the airport so you don’t have to rent a car.
Try pricing your hotel through Dvcrentalstore.com. You’re essentially renting points from an existing Disney Vacation Club member. I know they have some killer deals right now (40-70% off normal Disney prices). We’ve used it many times before and it works great.
We’ve stayed both on and off property many times and I would highly recommend on property. Adds to the experience.
We have kids your same age and our favorite parks in order:
Animal Kingdom
Hollywood Studios
Magic Kingdom
Epcot