Hi Georgia! How exciting to be planning your family's first Walt Disney World vacation! You're going to have so much fun!
The Disney parks and resorts have counter service restaurants available where no reservation is necessary. Reservations may be made at table-service restaurants. These restaurants will accept walk-ups if space is available, although you may experience a wait for a table.
Since you are visiting in the summer near the July 4 holiday, the parks will likely be quite busy, so I recommend that you make some dining reservations. Take a look at the park calendars to determine the operating hours of the parks during your visit, as well as the times of any parades or shows you'd like to see. Use that information to decide which park you'd like to visit each day, and then pick at least one restaurant in that park that you'd like to try, and make a reservation for lunch or dinner. If your plans change, you can always cancel the reservation, but you'll have it if you need it. Your vacation will be much more magical if you do a little advance planning to minimize the time your family spends wandering around looking for a restaurant with availability or waiting on a table.
I'd love to help you plan your first trip! Please come visit me again at the Moms Panel if you have more questions!