Living in Florida, a fishing kayak is one of the best ways you can spend your money!
As far as what boat to buy, it all depends on your budget. You want to make sure that you get a boat that is AT LEAST 12' in length, but I'd highly recommend going with a 13ft or 14ft boat since you're planning on going offshore. Also make sure that the boat is at least 29" wide. The extra length will make it a lot easier to paddle, and the added width will give you some stability so you can change positions without worrying about losing all your gear.
The models that I'd recommend looking at are the Ocean Prowler Big Game, or the Tarpon 140. You can find used models for anywhere from $300 to $600 to help save on the higher price tag of the brand new boats. Both of these models are time tested by anglers fishing in the exact same situations you're planning on fishing in.
The two boats above are also small enough that you can pack them into some of the lakes down there, or fish the canals for some peacocks when you don't want to head out offshore. They're easy to rig, easy to paddle, and easy to move around.
Remember to make sure that every piece of gear is tied down to your boat somehow, wear sunscreen and a life vest, and make sure that you've got some flares and a whistle when you head out offshore.
Tight lines, and good fishing!