Have a great time with the Goofy Challenge! Some of our Moms are getting very into running, and I'm training hard to cheer them on in their next running endeavor!
I would say the best park to start with is the Magic Kingdom. Aside from being "the" park people think of when they think of Walt Disney World, it offers the most options for the variety of ages of your boys. There is as much for the nine year old to see and enjoy as there is for the three year old. All three boys will probably love things like Buzz Lightyear, Haunted Mansion, the Speedway cars, and even the Tea Cups. Then you have things like Big Thunder Mountain, Splash Mountain and Space Mountain for the older boys; and It's a Small World, Peter Pan, and the Carousel.
EPCOT also offers something for everyone, and my girls - ages four, eight, and 18 - all enjoy things like Journey Into Imagination, Living With the Land, and now that the little one is tall enough, Soarin' and Test Track.
If your guys are animal or nature lovers, Disney's Animal Kingdom is a great option in terms of spending a free day. My nephews prefer EPCOT, but they loved Kilimanjaro Safari and Kali River Rapids. They also really liked walking around to learn about the animals and conservation efforts.
You can't go wrong with any of the four major parks, but I'd put Magic Kingdom and EPCOT at the top of the list. I hope you all have a great time!