My favorite time of year to go to WDW is late April into May up until Memorial Weekend.
If Easter is late, April can be crowded for most of the month. Many districts do have spring break into late April, again, especially Easter is late.
Early May up to Mem. is a safe bet.
The one thing to plan for is Grad Nights which see the MK closing early pretty regularly.
I love this time, its warm but not generally that humid. Obviously the closer to June, the more hot and humid it will get.
You have the Flower and Garden thing at Epcot.
If you want onsite and great pools, in my opinion all WDW resorts from the values up have great pools. Mods and deluxe's have sides and hot tubs. If you want to check out pictures of onsite pools, grounds, rooms etc, go to:
www.allearsnet.com They have slideshows of each and every WDW resort. Also, the Resorts Board here on disboards has FAQ threads on most if not all the resorts and lots of other information about onsite resorts. If you need offsite information, you might ask over on the Orlando Hotels and Attractions Board here on disboards.