In Italy all trains except Regionale trains require a reservation. You can make that reservation five minutes before you get on the train or five week. The ONLY reason to make advance reservations on line is to take advantage of any discount that could be available. The super economy fare in Italy can be very, very cheap but it is no change, no refund. The economy fare is decent and allows for one change with the payment of the higher fare. The base fare is available all the time. If willing to commit to a fix schedule then look at the super economy and economy fares.
The cheapest way (and of course, slowest) is the Regionale trains but they are slow. Buy a ticket at the station, validate date, and get on. No reserved seats.
PS All posting about the same time. On the discounts - It all depends on the time of day, train, etc. But base fare can be 60 Euro or more to Venice with a super economy tickets being as low as 9 Euro. And economy around 20 Euro. More than a slight discount. Discounts can be substantial.