Given the soil and climate of the southeast, specifically Florida, what hops would do I stand to get good results from growing?
The experts say that the "ideal" growing conditions for hops are between the 34th and 55th latitudes in both the northern and southern hemispheres. All of Florida is well below 34 degrees north latitude, so it is not an "ideal" location to grow hops.
The reason is that the days are shorter below the 34th latitude, so the plants don't get enough sunshine. Also, hops are very susceptible to diseases like downy mildew, powdery mildew, and others, and also certain bugs can attack the plants as well. In Florida where it's very wet, you'd be likely to run into a lot of issues with this.
However, that said, it is very possible to grow them outside this region, though you probably won't attain optimum results. A strong, hardy strain, such as Cascade, would be necessary. Cascade hops are known for growing well just about anywhere, but they can be susceptible to diseases if not carefully watched. My first year Cascades yielded a pound last year--which is not generally to be expected in the first year.
Tettnanger, Magnum, Perle, Brewer's Gold and Nugget are all known for being pretty hardy and disease resistant and might do okay in Florida.
Ones to avoid (known for being highly susceptible to disease): Hallertau, Saaz, Hersbrucker, & Spalt. There are others too, I'd suggest doing some further research before you pick a strain.
Growing hops is fun, I say give it a shot if you can still get rhizomes and see what happens.
It being sunny and warm where you are you aren't really all that limited. Just keep them well watered and aerated and you should be able to get a couple harvests from any hop bine you plant in a single growing season.
Of course it will take a year or two before you are really bringing in good multiple harvests.