I'll give this a try.

Realize that while I'm a Floridian, I've never fished around Jacksonville. From what I've heard, a lot of fishing there takes place in tidal creeks for redfish and spotted seatrout. While you can handle most trout and some redfish on a 5-weight rod, you might need a little bigger rod (7 or to be able to cast the bigger and often heavier flies (Clousers, Gurglers, etc.). As far as a reel goes, all you need is something that will hold up against salt water. Most often the reel's sole purpose is to hold the line at the end of the day. I've caught 30-inch reds that never got me into the backing and that I could hand-strip in. There are many less costly reels out there that can and will do the job.
As far as lines go, I use a Scientific Anglers Redifsh full floating line on my 8-weight and an SA clear sinktip on my 6-weight. I like to use the 6 when I'm targetting trout.

I'm not sure what's in the surf up that way, but I would guess you might encounter reds, flounder, whiting, pompano, black drum and others. There are striped bass in the St. Johns River, so I'm sure they migrate through the Atlantic.

You can Google some kayak clubs/forums in that area.

Hope this helps!