Jason this is a difficult question to answer because all of the Disney resorts are wonderful for children.
The Value resorts, All Star Music, Sports, Movies and Pop Century have fun theming for children but they do not have some of the common amenities found in the other categories such as refrigerators.
One of the most popular Moderate resorts for families is the Caribbean resort. There are playgrounds, beaches, and a newly refurbished theme pool for children to enjoy. This resort is quite spread out and if you don't have a room close to the pool or the central area you could be walking quite a distance to reach places you need to go. All rooms in Moderate resorts come with small refrigerators.
The Deluxe resorts offer the most amenities such as more elaborate pools, arcades, larger rooms, beaches, shops, and boating recreation opportunities. The Yacht and Beach Club has one of the best pools on property with a sandy bottom and toddler friendly areas but the Polynesian remains a favorite for many families. These resorts have refrigerators in all rooms at no extra charge.
If you need or want a complete kitchen set up then one of the villas might interest you. All have pools at their complexes and Saratoga Springs is a family favorite. This area has a themed pool as well that includes a water slide and toddler wading area, playgrounds, and some organized activities. You can also stay in one of the Fort Wilderness cabins which come complete with kitchens and that area is bounding with things for children to do.
You can read more about each resort and the categories by clicking
HERE. You will enjoy any of the resorts you choose and it depends on how much time you think you will spend in your room to what you are wanting to budget for the resort during your stay.