You've gotten some great information, so there's not much I can add.
As was stated, if you're only going to Disney World and no where else, you won't need a rental car and staying on their property is a big plus.
However, if you plan to go other places and only spend a few days at Disney World, then it would behoove you to get a rental car and stay off property.
We've been there and have also had alot of our clients go down there - with families, it's always been cheaper to rent a house and do our own thing. You can rent a private house through any one of several companies. And these houses have their own private screen-in pool, plus an outdoor grill. Benefits are that you can make your own breakfasts & dinners, if you like, thus saving considerable amount of money. It also costs less and provides more options and amenities than staying in a hotel.