Hurricane season lasts from June 1st to Dec 31st. Antigua hasn't been hit by one in quite a few years, and the reports from the NHC state that the problem areas this year seem to be the Western Caribbean and the Gulf of Mexico.
Having said all that, it's still just a matter of luck, and if you do get caught in one, look for a good hurricane party to ease the stress.
P.S. No back end to the season. Got caught in one (not in Antigua) on Dec14th.
Forgot to answer the question re. weather. By the end of October, it's started to cool down a bit. Any rain would be associated with tropical waves. Sea conditions would be good for all activities. And as the tourist season hasn't really started as yet, all prices (hotel, meals etc.) would be non-tourist, i.e considerably cheaper.