There are a couple of party boats that goes out of Ft Myers Beach, if you want to get off-shore for under $100. There are also split-charters for a few of the 6-pack boats there, which still isn’t bad. Get Away Marina is one of marinas there.
If you fish from shore, be careful about the fish you touch. Several small-looking fish have nasty teeth! Particulary the Mangrove Snapper. An 8″ fish will have a couple fangs over 1/2″ long, and has the same mentality as a snapping turtle.
If you want to try shore fishing, a number of marina’s and bait shops rent fishing poles. If you want to use one of your own, be SURE to rinse the rod & reel in fresh water as soon as you can once you are done fishing. The salt water is NASTY on equipment if given half a chance.
The two ways I would suggest fishing is with plastics on a jighead if you want to cast, and with shrimp on a carolina rig or under a popper.
Finally, if you want to keep anything, be sure you know the size limits and open/closed seasons as well as bag limits. Last I checked it was $500/fish if you keep something you shouldn’t.