If you don't mind paying a nominal fee, I really recommend touringplans.com; it has incredibly researched plans for each of the parks to help you make the most of your trip with as little time waiting in line (tours are tailored to your family: toddlers, just adults, teens, etc) . It offers advice on what parks to avoid, too.
If you'd rather not like to do that, I'd start by looking at the Park Hours
here. If you are a Disney resort guest, you can take advantage of Extra Magic Hours (EMH). We find taking advantage of the EMH in the morning a great way to visit many attractions while avoiding crowds (evening EMH are often quite crowded), but by late morning we usually "hop" to another park because of the crowds -- but this means that you needed to have purchased the park hopper option. If you haven't, I would plan to visit parks on the days when there are no EMH scheduled to move in the direction opposite of resort guests.
Specifically, on your first day (June 19) Epcot, Disney's Hollywood Studios, and Animal Kingdom don't have EMH; they should be good choices. The Magic Kingdom has EMH in the evening, so I'd avoid that park.
Also, you are able to make dining
reservations now which may help to decide which parks you will be at as well.
Since I've just got you started with some plans, if you have other questions please feel free to ask as many questions as you'd like.