First, the rail system reservation in Europe is not the US airline system that we have all been trained on. The schedules are available about three months out and not the year you get with the US. The only reason (and it can be a very good reason) for advance purchases is to take advantage of the discounts. But that locks you into a fixed schedule and some with restrictions like no refund, no change - like our airlines. You don't need advance reservations for a seat on the trains. Trains are so frequent and large that it is very rare for a train to be full. Bahn probably is the best site to view schedules - nothing else unless you are traveling in Germany.
Since you are going from Venice, look to trenitalia.com for purchasing tickets. It is a pretty simple site. Check the British flag for English, remember you are using the 24 hr clock and the European format for dates --- day, month, year. And some calenders start the week with Monday with Sat and Sun are the last two days of the week. Triple check your dates.
The fares in Italy are Super Economy, Economy, Base. SE can be very cheap but no refund, no change. If you do not understand that, look it up in the dictionary. Econ is changeable with a credit for the next ticket but no refund. Base is the walk up fare and fully changeable BUT once the train leaves the station all tickets are dead. The discount tickets are limited to certain trains, at certain times, and in limited numbers. All trains in Italy - except Regionale trains require a seat reservation which is assigned when the ticket is purchased. Only the Regionale trains are open seating and never discounted. Think of bus on wheels stopping at every town. A slow, very cheap, and can be a flexible way to go.