If you prepurchase a Supereconomy fare on line and miss the specific train you book (no matter which), you get no refund. So it is indeed a risk to purchase a discounted ticket online for a trip immediately after landing, because flights are unpredictable primarily because weather is unpredictable.
I generally buy the ticket in the spot at the FCO Airport train station for the first train available.
Even if the 15:08 is not available, there is a train departing from the city stations to Florence every 15 to 30 min.
You don’t need to take the expensive Leonardo Express to Termini. All trains to Florence stop also at Tiburtina. It is cheaper to take the regular Regionale from FCO to Tiburtina and catch at Tiburtina the exact same train to Florence. You don’t save time with the LE either. Because the Regionale takes a shortcut bypass to Tiburtina. Tiburtina is also a more modern and less crowded station where you are less likely to be robbed by the gypsies.
The full base price for standard fare to Florence is just over 50€.
www.trenitalia.com
Enter from FIUMICINO AEROPORTO
to FIRENZE SANTA MARIA NOVELLA.
use a date in the next week if your travel is too far ahead in the future. Timetables don’t change much.