First of all, don't be worried because of your age. Those same fears were mine when I first went to Italy 39 yeras ago.
You have plenty of time to make it to Florence before nightfall. Not to worry there.
Given what I understand of your situation I would do this. (1) Take a train to Rome. As earlier stated, go to Italian Trains
and check out the schedules. Do this before you leave for your trip. You really want an IC train to Rome versus the local.
When in Rome (Roma Termini station) get a ticket to Florence on the EuroStar (the fast train.) The EuroStar trains appear to run about every hour on the hour. Again, check trenitalia.com.
My investigations on this about a month ago indicated that you could buy, in advance, on-line. Checks yesterday afternoon indicated that this was true only if you were in Italy.
My wife and I had a discussion about this at dinner tonight. We decided not to worry about it as we never had a problem with trains when we lived in Italy. If second class is full, go first class. At our age, we have earned the difference.
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