Hi Jane,
How exciting to be planning your first Disney World trip! We very rarely have a car with us and find the Disney transportation system easy and reliable form any resort.
Our favorite place to stay is either the Beach Club Resort or the Boardwalk. Both are deluxe property locations so they are in the higher price range, but there are still great deals to be had depending on your vacation dates. We love these properties because of the amazing amenities, like the fantastic pools, numerous restaurants and shops, and the great things that go on at night like movies on the beach and the free entertainment on the Boardwalk. The bonus here is the location. Both resorts are within walking distance, or just a short boat ride to the Hollywood Studios and Epcot entrances.
At the moderate level, we really like the Caribbean Beach Resort, The rooms have all been recently renovated with either a Pirate or Nemo theme. The resort features a great food court area and numerous pools including the main pool which was remodeled recently and offers a fun slide area and a very cool zero entry pool complete with a squirting pirate ship. Tons of fun here!
Now if value is in your budget, then I would have to go with Pop Century. My boys love the oversized decorations and the food court is one of their favorite places to eat. The rooms are comfortable but smaller than those at the moderate or deluxe price points but should comfortably fit your family size. The value resorts do tend to be the most crowded since they are less money and bigger properties. The drawback here is sometimes longer lines for the Disney buses.
You can find additional information on the various resort choices
here. Good luck and happy planning!