In the past I have had all reservations and tickets purchased but we will only need one train ticket. Is it problems for 1st class purchase at the train station on day of travel?

I doubt you will have a problem, especially only for 1 ticket. In the worst case scenario and 1st class is sold out, it's only a 90 minute trip and 2nd class isn't unpleasant.

You can use the ticket machine at the station if there are queues at the ticket counter. The 1st option is to choose the language you want and then follow the very clear prompts.

I have traveled Italian trains for years with a first-class railpass and have never ever had any problem getting the necessary seat reservations even on the day of the train. You can buy your ticket in any Italian train station like at airport train stations - just be sure of exact date and travel time as tickets come with seat reservations. Full fare walk up tickets can be changed but it can be a hassle and take time.

I have found the station ticket machines to be idiot proof - at least I could use them.

It would be considered highly unlikely that all first class seats between Rome and Florence would be sold out on a particular train, although this might happen the day before Christmas, etc. Even so, trains on this segment leave every 10-30 minutes on average.

It'll be cheaper, of course, if you go to www.lefrecce.it and pre-book a super-economy ticket, than paying th full 'base' price on the day...