For Value I would choose Art of Animation- the theming can't be beat, it has the best pool and so much to explore throughout the resort. Pop Century is a great second choice for convenience, it's a short walk from Art of Animation so you can still explore it, it has an great food court and very efficient bus service.
For Moderate I absolutely love Port Orleans Riverside- relaxing for adults, fun for kids, tons of activities and a wonderful pool. It's also stunningly beautiful.
For Deluxe, my personal favorite is Animal Kingdom for the sheer beauty, the unique activities, the incredible food, the animals and the overall experience of feeling like you are somewhere completely different from any other resort. However, if you are traveling with children that young, I would instead recommend the Polynesian. I truly love that resort as well and the convenience of being on the monorail loop is fantastic. There are so many fun things for adults and children to participate in and it has a very relaxed vibe. Great food, great pools and you can view the fireworks from the beach! You can also easily take the monorail over to the Contemporary and Grand Floridian to dine or participate in certain activities there.