Hi and welcome, Aaron. I'm in Sarasota, too. What direction does your lanai face? All herbs pretty much need full sunshine to thrive, so be sure you're going to have enough sunlight for them before you invest in plants, planter and that awesome plant stand. (I'm going to get one of those next time I'm at IKEA too!) If you face north or east, for instance, you might not really have enough sun to grow herbs successfully. They'll be lanky and unhealthy.
Yes, those pots are going to be awfully small, once you get things going and your herbs start growing. But, a whole bunch of different kinds of basil, for instance, might do ok in those small pots if you keep them trimmed so they don't get too big. You are definitely going to be watering every day (do it in the morning!! very important) and I'd advise you to get white or light colored pots as well, to keep the roots of your plants a little bit cooler. Btw don't make the mistake of using "Moisture Control" potting soil. It keeps things much MUCH too wet here as the moisture beads gather water from the air here. It's good for dry climates but not for Florida!
Some herbs don't grow awfully well here in the summer anyway, due to the high humidity and hot, stuffy nights. You might be well advised to wait until around the end of September to plant things like lavender, sage, thyme, and mint. They like cooler temps, and really don't like the humidity. No promises on chives and other onion-y things either.
I've had good success growing rosemary, but it will definitely need a much bigger pot than those. It grows into a nice small shrub quite quickly. Maybe see if you can find a tall square pot that will tuck into an outer corner of your lanai?
