I'm a teacher, so always have to follow the school schedule. We regularly go President's Week and have various times in the summer, between Christmas and New Year's, and Easter. Not sure how late you start the school year (I don't start until after Labor Day), but that last week of August/the week before Labor Day is great as far as crowds go - the weather is hot and typical summer Florida awful, but as long as you're prepared, the low crowds will make it well worth it. That's honestly when I recommend most people who have to follow a school schedule go if they can. July and up until mid-August are terrible weather and terrible crowds, so avoid that if at all possible. My spring break is pretty much always the week following Easter - the later in April that falls, the lower crowds get throughout the week (Easter weekend itself until probably around Tuesday is packed). When Easter is earlier it tends to be more crowded because it overlaps with more spring breaks. Weather around Easter can also be unpredictable - you can have beautiful, comfortable weather and no rain, or it could be hot and humid and rainy, so that makes it a bit of a gamble. President's Week is also jam packed with crowds (especially if it coincides with Mardi Gras) - but the trade off is mostly pleasant weather which can make it more manageable. Christmas will be absolutely packed wall to wall people, but nothing beats the magic of Christmastime at Disney and again, you're more likely to get pleasant weather, which makes a huge difference when it's crowded. I imagine the situation around Thanksgiving would be similar.
Ultimately it's pretty much going to be a trade off of crowds vs. weather. As long as you go in prepared for it and with a good strategy to manage either, you'll have a great trip. FWIW the end of August will also be the least expensive time to visit because it's considered off-peak. All other times discounts may be difficult to come by.