My wife and I have been going to WDW every year since we were married. We do it in celebration of our anniversary, which is the last week in April.
Crowds are unbelievably light during this time of year. We have, literally, done every major ride in MK before noon several times. If you get there within a few minutes of park opening, there will be absolutely NO lines to get on anything. Last year, we rode POTC, Big Thunder Mtn, Small World, and Space Mtn without a single second of wait time, all before we went to breakfast.
Here's a hint we learned at Soarin' and then noticed all rides were like this. There is a minimum wait time they will leave on the FastPass rides of usually 30 minutes. If you don't see a line, ignore that and walk on in. It may very well be that the wait is below 30 minutes, and a FP would hurt more than help. When Soarin' said 30 minute wait times, we walked up to the second or third place in line. POTC showed 25 minute wait times, and there, literally, wasn't a soul in line ahead of us. That's a weird feeling, too.