Welcome and happy planning!
All Star Music Suite (value) is nice and sleeps up to 6.
The value resorts are cutesie w/ oversized iconic images and it's a "motel-like" atmosphere w/ only quick service ( like fast food, but a bit better) meals, bus service only, an outside corridors only.
The Cabins @ Fort Wilderness IMHO are the best "bang for your buck". It sleeps up to 8 , and has all of the comforts of home. There is an "internal" bus system to take you to the main pool complex and food area. May I recommend making reservations for Hoop Dee Doo Musical Revue!? Some people rent golf carts to get around, but that can get pricey!
2 rooms anywhere ( especially Port Orleans, Caribbean beach, and Coronado Springs) might be worth it. All of the moderate resorts have that "motel" feel as well, but are just a bit more "spruced up" w/ a slide at the main pool complexes. They also have sit down table service restaurants. I enjoyed both Port Orleans Riverside ( the boat to Downtown Disney) and Caribbean Beach ( lovely).
Of course the Deluxe accommodations are the best!
But, the most expensive!
It's mostly about convenience and transportation. My favorite is Wilderness Lodge, but your family would have to get 2 rooms, or rent a Villa. Deluxe resorts have "signature" restaurants on property, and those are so awesome! ( expensive, but if you're on the dining plan, it's 2 table service credits). I truly enjoyed the Polynesian as well. the Spirit of Aloha Show is a must do at least once, and it has the best restaurant on property IMHO: 'Ohana.
Overall, it depends on your choice of "theme", and which park you think you'll spend the most days/time at. If you're going to be mostly @ Magic Kingdom, then Grand Floridian, Poly, Contemporary, or Bay Lake Towers is perfect, but very pricey! Wilderness Lodge and Fort Wilderness have boat launches to the Magic Kingdom!
If EPCOT or Hollywood Studios is your park, then stay at Beach Club, Yacht Club, or Boardwalk ( villas).
If Animal Kingdom is your park, Animal Kingdom Lodge is a wonderful place to stay! You'd need a villa at Kidani Village, but watching the animals ( savannah view ) is worth it if you like to do that kind of thing.
Welcome to the boards and good luck w/ your decision! I'm sure whatever you decide, you'll have a Magical time!