As you probably already know, nice rentals go FAST.
You have to be very careful about renting from an individual owner because there are many that are in pre-foreclosure status and you may have to move soon. Also your deposit may be difficult to collect.
So, if you are just renting "temporarily" until you are in a position to buy, you may want to consider renting in an apartment complex.
If you have sufficient credit and income and just need downpayment money to buy, the State of Florida has bond money and you can get up to $7,500 to buy a house. Nowadays it's usually cheaper to buy than rent a house--especially in LOL or Lutz.
If you have other credit issues that prevent you from buying right now, there is the NACA purchase program: http://www.NACA.com
Also my tenant recently had a short sale and bankruptcy but was able to buy a home only 3 months after the short sale with a mortgage from GTE credit union: http://www.GTEFCU.org
If you decide to go ahead and rent from an owner, it's not unreasonable for you to ask for recent copy of the mortgage to be sure the landlord is up-to-date before handing over any money!
All the best,