Michelle,
Yes, you can most certainly wait and purchase the tickets when you arrive in Rome, a day or more prior to travel. The tickets will include the compulsory seat reservations. I've done that many times, but the disadvantage to that approach is that you'll likely be paying *Base Fare", which is the highest pricing tier and currently ranges from €44 to €109 PP. I've always found the least expensive seats in second class are just fine.
If you purchase tickets in advance and choose Super Economy, the current price on that route appear to be €29 PP. However, you MUST be willing to commit to that particular train, date and departure time as the reservations are specific. If you're caught without valid reservations for the train you're riding on, you'll likely face hefty fines which will be collected on the spot! The Super Economy tickets are non-refundable and non-changeable so if you miss your booked train, the tickets are worthless and you'll have to buy more.
There's a quota for the Super Economy tickets and once that quota is reached for a specific train, the price moves up to Economy which also has a quota. When those are gone, the only option is Base Fare. The concept is similar to the "sliding scale" used by many budget airlines.
This may sound complicated, but it's all rather easy once you've done it a few times. Note that you can also use the competing Italo Treno high speed service between Rome and Florence, although in some cases their trains may depart from the Roma Tiburtina station. An easy place to purchase tickets online is at www.captaintrain.com (very user friendly website), and they sell tickets for both Trenitalia and Italo.
Buon Viaggio!