I am a planner by nature and in my 33 year career as a city planner. I always purchase train tickets in advance, EXCEPT on flight arrival days.
My husband and I have flown into and out of FCO before, we have been in Roma Termini several times, and we fly with carry-on only. We are pretty familiar with the drill. We are both in good physical condition (56 and 68).
We are flying into Rome next week, taking the Leonardo Express to Termini and we will purchase the Express tickets via the app after clearing immigration. While in route to Termini we will purchase our train tickets to Florence via the Italo or Trentalia apps based on which system provides us the best options in terms of departure time and ability to book seats. If you look, you will see there are hourly trains from Termini to Florence SMN via both train systems.
We are comfortable navigating Termini, but it is rather large and crowded. For us, even being familiar with it, I would NOT book a train ticket to Florence that was departing less than 20 minutes (30 would be better) from our expected arrival time via the Leonardo Express. I do agree with the other poster regarding luggage and having to possibly traverse from the far platforms for the Express, to the last platform on the other side. Unless Italo or Trenitalia have some type of assistance you will have to schlepp your own luggage onto the train and stow it. You will definitely need to confirm with Italo or Trenitalia regarding assistance with luggage as I have no familiarity with this.
The issue of luggage is the same with the Express. You will have to get it from the platform onto the train. While the Express seats are not as comfortable, they do have more luggage storage in the cars. You may also need to confirm the Delta porter will take you to the train station at FCO - it is well outside Terminal 3.