Welcome, Sam. Looks like you already have a few nice raised beds in place there. They'll need clearing out, and heavy amendment with organic materials to loosen and enrich the soil so it will hold moisture and nutrients. This is an ongoing process in Florida because the intense sun, heavy rains and humidity break down the organic content of the soil very quickly and the plants use it up or it is washed away by rain and irrigation. Plan to add new amendments every fall before you start the new garden. Gardening season for veggies is mainly October through May here. Summer is for cleanup, resting, planning and collecting new materials.
Do not buy anything labeled "Garden Soil" or "Top soil". They will be mostly sand and not worth paying for - you probably already have lots of sand. Buy 100% organic material to amend your beds - mushroom compost is excellent, not expensive and available at most good nurseries. Otherwise, a raised bed mix can be good as well if it says it's all organic stuff.
Another wonderful amendment I've used is alfalfa pellets - they are horse food available at any feed store in 40lb. bags. They enrich the soil, give a very mild, slow-release nitrogen boost that is great for seedlings and new transplants, and break down to boost the micro-biome.
Tomatoes can be planted starting mid-September to mid-October and if you will plan to protect them from the occasional cold fronts we get in Dec and January, you can harvest tomatoes from November to June. Choose different varieties - a quick, short season one, a cherry or grape type, and a long-season slicer. Tomatoes pretty much don't set fruit here in the summer, the flowers just drop, and it's hard to keep the plants healthy through the hot weather with disease and insect problems ramping up tremendously once the nights are warm.
Green beans are great, but be prepared to spray with BT to keep caterpillars at bay. It is an organic-approved, targeted solution that doesn't kill anything except the caterpillars that eat the leaves of your plants. Good for squash, cucumber and melons as well.
I'd advise you not to go for growing corn. It is a tremendous space hog - plants a foot apart, rows 2ft. apart - and needs good soil, a ton of water, fertilizer and does not bear much for the space and resources it needs. You must plant a large section of it (not a row) because it is pollinated by wind, and if you only plant a few plants it's unlikely you'll get any cobs. The area of lawn in your picture is about the size of a corn patch you'd need to get a decent harvest.
Peppers, either sweet or hot, give a much better return on your small space and resources. They can be planted in fall as well, (need protection through winter) but better to start them in February for a spring into summer harvest. They, along with basil, eggplant, okra and a few other tropical veggies will go through the summer heat quite well, if you can keep them healthy.
This book has been my go-to reference for growing edibles in Florida ever since I moved here. (it's dog-eared and taped together) Highly recommend you get a copy (there are a couple of newer editions) and you'll have some good info for just about anything you want to grow in Florida.
