Resort for resort's sake: choose a deluxe resort, as those have the most comfortable rooms, the best pools & other amenities. Can your children swim? If so, I recommend Beach Club or Yacht Club, due to its extraordinary Stormalong Bay pool complex (sandy bottom pool, huge water slide, sand castle building area, mini-lazy river, waterfall, etc.) The lazy river is deep, so if your children aren't independent swimmers, that might not be the best choice. It's also on Crescent Lake and across from the Boardwalk, which has various minor attractions available, and is not far from Fantasia Miniature Golf (a leisurely walk or a short drive).
If your children aren't independent swimmers, I recommend Grand Floridian, which has a very nice though less spectacular pool with no deep areas, and also has great views and easy access to many good restaurants. Riviera would be my 3rd choice. Contemporary and Art of Animation have very mediocre pools, so they aren't the best choice for a warm weather resort trip.