Around here we refer to those as "The Common Gecko" (House Gecko) "The Common Lizard" (Brown Anole) and "Hey neat, they arn't extinct yet!" (Green Anole) :rofl:
Not sure on the exact requirements for keeping House Gecko's, but from what I've seen of outside they seem to prefer dark quiet areas. Doubt temperature or lighting will be an issue. But they may not be all that interesting to keep since they don't really seem to like being in the open.
Also, with Anoles the way you tell males from females is you look for the throat fan. Males have a redish/orange fan on their throat that they display for various reasons.
Also also, Florida does now have Knight Anoles so not all of the green ones are Green Anoles. Not sure if they've spread out of South Florida though.