I live here on Story and routinely fish here. The other advice is spot on. Also, people have caught some fairly large drum out here late in the season by reading the beach well. Croaker are always easy.
Make sure you're eligible to come on the base in the first place. I know that should go without saying, but I'll be out there and will routinely kick people out that shouldn't be here. This is more or less a tip for other people reading this: Ft. Story beach is not public access. Eligible ID card holders only... And their guests. So if you want to fish it (there really are better places, though) find your nearest military buddy and have them escort you on.
Honestly, though, the fishing isn't great here. I fish here because I live right on the water, so it's a very convenient thing. If I wanted better catches I would just go elsewhere.