to Florida, and to ATP, Heather.
on the compost, there's nothing that will improve your soil more than adding lots of good compost. It does indeed break down fast here in the heat and humidity, though. A good idea to resolve to just top dress the beds each year with some compost to keep the fiber component in the soil up. Our soil is mostly sand here. As far as mold, fungus and other natural stuff, an outdoor bed in your Florida garden will have all that stuff in it, and it is healthy soil if it does. We have every mold and fungus spore known to man floating around in our lovely warm, moist air so . . . it's like the bugs, you just have to get used to having them around. It's Nature here - all that stuff lives here for the same reason we do, if you think about it.
First question I have is, what direction does that side of your house face? The amount of sun the bed gets will be the first determining factor as to what you'll be able to plant and grow well there.
Next question, is there an overhang over top of the bed all the way along? If so, it won't get much rain and you are faced with putting in some sort of irrigation, or hand watering the bed forever.
Good first instinct to go with native plants, but since that bed is right in front of your window, you will want to have something colorful and nice to look at all year 'round. Most natives go dormant in the winter here, (yes, we do have 'winter' - as far as the plants are concerned, when the nights get into the 50's they start to slow down.) Natives are in their glory now, in summer and through fall. You might plan a basic native flower bed there, and augment it with some annuals in winter for color.
For future reference, IF you end up buying a home of your own, it's not a great idea to have a flower bed that will need watering right up next to the wall of the house. Since this is a rental, there's nothing you can do about it so may as well enjoy it. If you buy, keep plantings at least 2ft. to 3ft away from the house. The dryer you can keep the soil next to the house, the less problems you will have with insects and mold getting into your walls.