Floridians hate to hear tourists taking their prizes! That is my experience, (almost a lifelong Florida resident), don't trust the locals!
The protected marine sanctuaries are in john pennikamp park. While you can't collect at all there it is worth the trip for some AWESOME snorkeling. Before you get down here get yourself a recreational license. DO IT NOW, your time here is a precious commodity. Collecting aquarium critters brings all sorts of attention from everyone. You will be surprised. Don't take liverock or hard corals, (or seagreasses, long spined urchins or anything else protected), they come with HUGE fines. For example a local LFS guy was caught taking liverock and he was fined 250k. Don't lose a house over a piece of rock. Almost everybody in the Keys will be proud to turn you in for it, just be careful and stay after crabs, snails, fish etc... check you fwc regulations with the link given to by the other member. Same with hard corals, you might as well start selling drugs.
Now that the doom and gloom is over, you will have a blast! If you are going after fish and want to be sporting, get yourself a hand net with a good strong rim, and a long basket. Don't waste your money on a slurp gun, they suck. The bridges provide good fishing, but anywhere you see with good structure will be teeming with life. That way everywhere in S. Florida. If you are going to net fish don't try to slowly get them in the net with patience. This never works! You MUST pounce on them, catch a wave and use the extra speed to get the jump on them, or you will end up empty handed. Additionally you must lead your fish, don't swipe where it is at, swipe where it is going. You will also want to swipe with the rim parallel to the floor, twisting it at the last second to catch the fish. This takes practice, try to learn the move before you get here. (Practice in lakes maybe). They also make fish traps...lame.
If you are having a hard time catching with the hand net, (you will, it is hard swipe often), then work the tide pools. (Tides are the key to any fishing experience, you should know them regardless). On a low tide find some good rocky tide pools, and look for fish taking shelter. If you can't net fish this way, it is hopeless for you I am afraid.
I don't collect in Key West, (so expensive to stay down there), I am up north more in palm beach county. If you come here I can put you on the money spot, although you won't get any info on soft corals from me. They are terribly overfished and I can't wait for FWC to protect them. Please don't be that guy who comes down here and helps to ruin the treasures of our state to save $8.