Laura, re. your itinerary--have you thought maybe about visiting Florence first and then heading to Rome? Would save you some time/backtracking.
I found it very helpful to print out train schedules before leaving home with several times that would maybe work for us. On past trips we always had a rental car but last summer used the trains and it was very easy to do. Trenitalia will update their schedules in June but for the most part you should be able to check schedules now.
www.roninrome.com has lots of useful information on train travel in Italy. Also R.S. Italy book has train info too with a sample ticket you can study so you know what the words on the ticket mean--carrozza, Posti, Finestrino, etc.
Just remember to validate your ticket on the platform before boarding the train. We saw people getting fined on about every train we were on. Let me know if I can provide further info.