Last year, we were faced with this same issue. We first booked Caribbean Beach. We then realized how enormous it was. We then looked at French Quarter and booked it. We stayed there and fell in love with it. In fact, we are staying there next week! It's very small, but that's a major plus in my opinon. Getting a preferred room isn't important, as the room furthest from the lobby is only a mere 2 minutes away. And I'm not kidding!
Seeing you have a 7 year old, after a long day at the parks, no one wants those long walks back to the room. You eliminate that problem at French Quarter. Plus, Caribbean Beach has 12 bus stops! Riverside, I believe has 4 stops. French Quarter has only one.
I think staying at French Quarter would be your best bet. Let it be noted, however, I have never stayed at any of the other two resorts.