Should I wait until I get to Rome to buy train tickets from Rome to Florence for travel in May or should I do it on Line. We will be in Rome for 3 days prior to the train travel.
You can easily wait until you get to Rome to buy tickets. The only advantage of buying from Trenitalia early is to see if you can get the Premium fare which is a 15% discount. The Premium fare has to be purchased 7 days in advance so you can't wait until you get there for this one. From America, you can only do this with a Visa card that you have registered with Visa's Verified by Visa program.
You may also, when you arrive, find there are still some Amica discount tickets for the IC trains, if you don't mind the fact they aren't as fast as the AV and ES trains (the IC trains are cheaper to begin with.) Amica fares are 20% off and can be purchased (if qualifying seats are still open) up to midnight the day before you depart.
I would wait till you get to Italy unless you're traveling on a public holiday.
Thank you all for your words of wisdom and advise. We are looking forward to our vacation, we will be there a full two weeks.