If your SLR or HOR is the state of Florida, then that is what you should enter for your resident state.  Where asked if you lived in any other states you should indicate NO since you are active military.  Where asked if you made money in any other states and your military pay is your only income you should indicate NO.

You would not file a Georgia state tax return if your resident state is Florida.  Florida does not have a personal income tax so there would be no Florida state tax return.