Hi Stephanie,
Beginning with figuring out which resort you would like to stay at is a good idea, as is staying at a Walt Disney World resort. By staying at a Walt Disney World resort, you can take advantage of Disney transportation to and from your resort, as well as perks for Walt Disney World resort guests such as Extra Magic Hours.
With a group as large as yours, and with the configuration that you have (less adults than children), I am going to recommend that you consider staying at one of the Disney Vacation Club resorts. At a Disney Vacation Club resort, your whole traveling party will be able to stay in one villa. This would be a two-bedroom villa. You could consider Bay Lake Tower at Disney's Contemporary Resort, Disney's Animal Kingdom Villas - Kidani Village or Jambo House, Disney's Beach Club Villas, Disney's BoardWalk Villas, Disney's Old Key West Resort, Disney's Saratoga Springs Resort & Spa, The Villas at Disney's Wilderness Lodge, or The Villas at Disney's Grand Floridian Resort & Spa. Although these are all Disney Vacation Club resorts, there is typically inventory available to guests who visit using traditional payment methods, such as credit card or cash. In order to check availability for the dates you are considering, you can call Disney at 407-W-DISNEY (407-934-7639).
Two-bedroom villas at Disney Vacation Club resorts include a full kitchen and a washer and dryer, which I find wonderful to have on vacation. If I was going to recommend one to you, I think I would choose
Disney's Old Key West Resort. This resort has some of the largest of the two-bedroom villas, and it also often has villas available for traditional payment methods.
Please do come back if you have any further questions, Stephanie. I would love to help you as you plan your magical vacation!