My vote is for as early in June as you can go. I have been just about every week in June in the past and the crowds are definitely the best that very first week. After that, more and more kids get out of school and the parks get increasingly crowded.
The only thing is you'll definitely want to avoid the Magic Kingdom that first Saturday as that is usually the "official" gay day and the crowds will be outrageous. Other than that one day we didn't find any excessive crowds during our trip the first week of June a couple of years ago.
You'll have fun whichever week you choose, it's hard not to at WDW!!!