I personally wouldn't hesitate to book a trip during the 1st part of May since you will be beating the summer crowds.
Choosing a resort can be an overwhelming experience, & it should begin with your budget. WDW offers 3 levels of resorts: value, moderate, & deluxe. The
value resorts are themed around sports, music, movies, and decades; they offer fewer amenities, but still keep you immersed in the Disney magic. The All Star Music resort also has family suites (sleeps up to 6, 2 bathrooms, kitchenette, 2 rooms).
The
moderate resorts have larger rooms and more amenities, but the cost of the resorts will increase as well. A favorite resort is the Caribbean Beach Resort's because it has pirate themed rooms. Just an fyi, some of these resorts can be quite large.
The
deluxe resorts are the most costly with the most amenities & are closest to the parks. When our children were little, we loved staying at any of the Magic Kingdom resorts because it was so easy to come and go from the Magic Kingdom to the room for naps/breaks. My sons also love the Beach Club/Yacht Club because of its AMAZING sand-bottom pools as well as the Animal Kingdom Lodge where animals are right outside of your balcony.
So in a nutshell, once you decide on your budget, you can visit each of the resorts online to see which your family would like best. Also, discounts are sometimes available & a reputable travel agent would be able to help you with. You may want to also sign up for newsletters from www.mousesavers.com & www.allearsnet.com to keep on top of news and discounts.