Some of the prior information is slightly misstated. Visa and MC without the chip will work just fine nearly everywhere in Italy with the exception of automated toll booths and filling stations. Will work in the ticket machines. AE is not readily accepted anywhere except at high end restaurants and hotels. This is one time you can leave your AMEX at home.
Be very careful and know your pricing when using the Rail Europe site. It is a travel agency with significant up charges on the tickets and reservations that they sell. Personally believe that RE should be avoided.
Trenitalia will not accept American credit cards because of fraud issues. There are some work arounds but not worth the effort. There are 53 trains a day between Florence and Rome you will not have a problem walking on to the next available train. Buy your ticket to Florence at the ticket office in the airport when you buy you LExpress ticket.
There are practical no discount available for advance purchases for Italian trains so don't worry about buying early. There is an Amica fare (-20%) but is limited to just a few seats 24 hrs in advance. And some recent postings have suggested that this fare has become even more restrictive and less available. Compare to most other railroads, the Italian system is cheap.
Relax, Italy is the easiest country for rail travel.
The blink technology on Am credit cards is not the same as the chip technology in European cards. The blink on you American cc will not improve acceptability.