Hi Mary Frances,
You'll definitely want to stay on Disney property because there are so many benefits available to onsite guests. This includes complimentary transportation from the airport and throughout the Disney property, access to "Extra Magic Hours" (more time in the parks before it opens and after it closes to off-site guests), the option to purchase the Disney Dining Plan and much more.
Disney has so many wonderful resorts to choose from and which one in particular I would recommend for you really depends on your budget and preferences. I suggest that you start looking at the
accommodations here and narrow down which category you most prefer (Deluxe, Moderate or Value). In the Deluxe category, there are numerous fantastic options. The Grand Floridian, Polynesian and Contemporary are all on the monorail and are therefore close to the Magic Kingdom and Epcot. The Yacht and Beach Club and the BoardWalk Inn are in close proximity to Epcot and Hollywood Studios. The Wilderness Lodge and the Animal Kingdom Lodge are a little bit further away, although the Wilderness Lodge is a boat ride from the Magic Kingdom. All of these resorts are highly themed with many amenities. If you are interested in a value or moderate resort instead, you'll find multiple great choices there as well. After you have narrowed down your interest by category, we'd love to answer any specific questions you have about the various resorts and can help you choose between a few of the ones you are most interested in.
Have fun planning and hope to hear back from you soon,
Kaylene