Check Your local and State Game Laws to see what Calibers are allowed for Deer Hunting in Florida.I've read that the Deer are much smaller there so You may be able to use a .223 which would have lighter recoil for a Younger Hunter,the next size Caliber I highly reccomend would be the .243 that several others mentioned also.
For a good quality and reasonably priced Rifle I would look into the Savage Axis Youth Rifles with the scope package,plus they have the newer models this year that have the Accu-Trigger so for a little more money You can get a better trigger that's adjustable.They have the plain Black Synthetic Axis,the XP Camo and the Cool looking Pink/Black Camo Muddy Girl Rifle also!