You have three levels of fares in Italy for all trains requiring a reservation. Super Economy, Economy, and Base. The SE and Econ tickets come with restrictions and limited quantity. Probably more SE available on the 6am train than on the noon train. Once the limited quantity is sold, that is it. Buying at 120 days will insure the most availability. At 60 days, who knows? All could be gone or some might still be available on limited trains. The SE offer significant discount, Econ less so, and, of course, Base is the standard fare.
One exception of all of the above. The Regionale trains are open seating - no reservation. Get on and go. If you cannot find a seat you stand till one becomes available - general not a major problem. Regionale trains are one price, never discount, and cheapest but also the slowest since they make lots of stops. Since your trip will involve various trains from Regionale to high speed (Florence to Venice, for example) and IF you are willing to lock into a fixed schedule, then buy the high speeds trains now to take a advantage of the discounts. These tickets will be non-refundable and non-changeable. For the R trains, buy the tickets at the station. You can only buy R tickets seven days in advance on line so that probably is not an option for you. However, never buy an R ticket on line.