If possible I would avoid Sept like the plague. At best you're going to get regular afternoon thunderstorms and much humidity.
In December (early) you do run the risk of hitting a relatively cold snap (temps in the low 60s) but it's unlikely to hit for long. More usual would be low 70s for most of the time. Even when it's colder, it's unusual to be rainy and cold. Dress wise you might be in need to a fleece (sweatshirt) jeans and if you REALLY feel the cold gloves, but I've found a thich(ish) T shirt and shorts are ok at that time of year most of the time.
As as already been said early Dec is pretty good for crowds (not too many people) although the park hours tend to be shorter. Crowds start picking up about Dec 17/18th and are madness for Xmas week itself. As badger says, they can get busy at weekends nearer to Xmas as well, so avoid the major parks. I think Florida schools should break up about Dec 16/17th.
IMHO the best times of year to go are late Oct/Early Nov or late April to May. But if you're limited on times I would say Early dec is your best choice of the two.