Sounds like you've got three problems--drainage, tree suckers and privacy. As to drainage, I always recommend that you at least consult with a professional landscaper. You could make some big mistakes on your own that will cost you more in the long run. That said, you could put in a rain garden where the water pools. A rain garden is simpl a shallow basin set a little below the ground level and filled with water-loving plants to catch the runoff. For the tree problem, I know that suckers from roots can be a problem--about all you can do is cut them off at ground level on a regular basis. In addition, I would put in some ground cover to give the tree roots protection and give the suckers a little competition. For privacy plantings, a combination of trees and shrubs is best. Go to Floridaplants.com for a list of things that grow well in your area.