By far the easiest form of hydroponics is a simple soilless drain to waste system. Just get some pots, a irragtion system (55 gal drum with feeder lines), some grow media like promix HP, and fertilizer and you are ready to grow. Maybe a ph meter to get your ph down to 6 after nutrients are added.

This form of hydroponics is the easiest, but does not save as much water/fertilizer as other systems would, but it saves way more then soil grown does.

hey olddaddy. Welcome to the forum.
You may find this guy's page helpful. dig around a bit; construction instructions are there.
He doesn't post here anymore, but I believe he was growing in florida as well.

Hi, welcome to the world of hydroponics. You will probably get lots of input as everybody has their own ideas on what is best. Just remember the most important thing about hydroponics is keeping the nutrient solution at a temperature that will not damage the plants (below 80ish and above 65ish). You are able to keeps plants outdoors longer than traditional gardening if you can control the nute temp by burying it or adding a cooler or heater.
Each system has it's strengths and weakness' so YOU have to do your homework on what works best for you i.e. $$$, location, space, type of vegis grown, time you have to spend etc.
That said, I have utilized several different kinds of systems. I have had both NTF and flood and drain in a 4 and 6 inch tube. I have grown pumpkins in a 16 gal rubermaid tote utilizing a bubbler system (DWC).I have a drip system in a 5 gal water bottle. My favorite system so far is a flood and drain in half of a 55 gal barell sort of like the barellponics. Hope this helps, good luck!