The only down side of September is that some of the services close at the end of August. However the major ports will all be going strong with plenty of room at facilities. September nights are comfortable, unlike July and August when temperatures tend to be on the hot and muggy side. Also, from a sailing perspective, there is more wind in September than in July/August. October can have great sailing, but some of the nights can be "cold", particularly toward the end of the month. There are fewer facilities available in October, but the number of boats in the harbors is also way down from September.
As far as storms are concerned, I wouldn't worry all that much. Hurricanes are 12 hour events here. If you pay attention to the track you can pick a harbor where a hurricane will be a non-event. If you panic, you can always get a quick haul at one of the yards. Most insurance policies cover at least half the cost for a named storm. I have ridden out every storm for the last 16 seasons on a mooring without any problems