If you are traveling from Rome to Poggibonsi, you will be on two different trains. On the most common runs, the first train will be a Frecciarossa from Rome to Florence. The second train will be a Regionale train. No economy or super economy tickets on a Regionale train. They are never discounted. No seat reservations either. You buy your ticket, validate the ticket before boarding, board the train and find your own seat. If no seats you can stand. This is different for your fast train where you must have seat reservations.
As for your Frecciarossa fast train, it will cost you 43Euro per person. This is the full base fare. Since you will pay full fare, you can easily buy the tickets when you get to Rome. I don't think that you can buy tickets online for more than five people anyway unless they've changed their policy recently.