Hi Robert,
I've visited Disney World for seven of the past nine years during late September and early October. It is actually one of my favorite times to visit. The weather is gorgeous, usually in the 80's, and we spend some time relaxing by the pool. The crowd levels are quite manageable, as a lot of students are just getting back to school so parents don't pull them out that early in the year. One thing to keep in mind that can affect crowds is the
Epcot International Food and Wine Festival which will be held from September 27 - November 11 this year. That does draw some crowds to the World Showcase section of Epcot, but is a really cool event that you won't want to miss.
You really can't go wrong with either choice (late September or early October). I suggest keeping an eye out for special offers. You may be able to catch a
Free Dining offer. In fact, there is one right now that is valid through September 25th. As long as you arrive by then, you can get the Free Dining throughout your stay. You'll want to book that quickly before it expires!
Wishing you a wonderful vacation! Please let me know if I can assist you further,
Kaylene