Time needed between Airport and High Speed Train

How much are you going to save by purchasing nonrefundable tickets? Your real risk is that your inbound flight is seriously late.
Just picking a random future date of Aug 1, the 11:35 Freccia to Florence is 41.90 EUR Economy 2nd class ticket. A Base fare ticket is 50 EUR. so you would only save 8.10 EUR per adult. That is not enough to justify the risk of being delayed and losing the Economy ticket and having to buy a new Base fare ticket. So I would just buy a ticket when you get to the airport train station. There are Freccia trains to Florence every 30 minutes that time of day.

True, but the SuperEconomy tickets cost € 27.9 per person in early August and the Speciale Frecce tickets only € 20.9
I bet Italotreno is even cheaper if you subscribe to their newsletter. If "we" is a family of 4 they could save 88 € or more.

The risk of a flight delay is real. I have flown from the US to Europe (and back) about 40 times in the past 35 years (I.e. I crossed the pond about 80 times) and in about 20% of cases the delay was at least one hour (in two cases the delay was over one day and I arrived a day later). Another thing to take into consideration is the possibility of back ups at passport control or baggage claim.
If the savings are substantial (and a Super Economy fare saves about 40%) and you are traveling with your family, then take the risk, however I would take a later train, because 2.5 hours are sufficient if everything goes smoothly but I would consider that tight. After the plane docks at the gate, deplaning, passport control, baggage claim, use restroom, walk to train station will take about an hour without any snarls. The Leonardo Express departs every 30 minutes, but what if you arrive just at the time it leaves the station? Then you have to wait 30 min for the next one. The ride is 32 minutes, but once at Termini you need to walk to the platform where the Florence bound train departs from (after you find out which platform). The layover at Termini should be at least 20 minutes to be safe. So, moral of the story, 2.5 hours is the proper amount of time if all planets align.

Thanks so very much for the great advice. Sounds like we need to give ourselves some extra time. Maybe we will choose the 1235 train instead. That gives us 2 more hours. So in that case I guess my new question would be could we plan on finding a place to have a great Italian meal somewhere with that extra time if we end up having time?

We have a similar overseas flight arrival at 8am and travel plan from Rome to Florence in mid-June. Instead of making the transfer from the airport into the Rome main train station, we booked the direct train on Frecciarossa. It departs from Rome Fiumicino Airport at 13:53 and arrives in Florence SMN at 16:11. We got a good deal by buying tickets in advance. If our flight is on time, it's possible we may have time to kill in the airport in Rome but if there are delays, we won't be stressed about missing our train.

Actually if you don't mind the potential longer wait, opting for the later 13:53 train, as suggested above, might be a better option. That high speed train departs directly from the airport and does not require you to switch trains at Roma Termini, so less stress in case of flight delay and less lugging of suitcases to transfer trains at Roma Termini. The train you board at Fiumicino is the one that takes you to Florence.

Of course if your plane is timely or early, you might have some extra hours to kill at the airport, but you can have lunch at the airport. There is Eataly at Terminal 1 now, among several other choices. If I remember correctly last July I went there before going through security.