Obviously you are going to do the ATPL Theoretical knowledge, as you won't be able to get the license until you have 1200 hours, 350 multi crew and a bit more.
Second of all hour building in Florida is oke, but something you shouldn't do in the Summer. It is way to hot and in every afternoon you will have severe thunderstorms. (when I say severe, I mean nothing you've ever seen in the UK)
When flying with an instructor under instruction the instructor is PIC. For the FAA you can log it as PIC (if you have a license) but EASA will not accept that.
With a fresh PPL, I doubt it would be safe to fly more than 3 hours a day.