We always go end of September and sometimes it can be busy but no where near like I have heard it can be other times. We never go to the parks on a weekend and use the fastpass for the more popular rides. We're going Sept 21st (can't wait).
We have been anywhere from about Sept 5-Oct 10 during various years. The lightest crowds are from early September with each following being slightly more crowded than the last. But even into early October it is quite manageable.