Did you see the board for European Rail Travel? I'm sure your first question has been asked by others. You will pay more if you wait, but at one month out, it may already not matter.
My family traveled to Rome, Florence and Venice this past June; we kept an eye out for the release of the schedule, so we could secure the cheapest fares.
We rode Trenitalia from Rome to Florence for about $25 per person (76 euros for 4 of us) and Italo from Florence to Venice for about $27 pp (84 euros for 4).
While our daily activities weren't always too structured, we had arranged hotels in advance so it made sense to buy train tickets in advance too.
Have a great trip!