Your parks wildlife (or parks and rec depending) should have a list of all banned species. you will need the scientific name to properly identify.
just because it is for sale in stores does not mean it is legal to own. Here in texas Apple Snails are on the banned species, but they are for sale at nearly every LFS in San Antonio. I have seen Asian Tiger "Lobsters" for sale at 3 different stores. I bought one, and a found out a couple months later that they to are on the banned species list here in TX.
it turns out that in FL you need a permit for Red eared sliders (turtle), and nearly all crayfish are banned but i didn't see anything about ADF