Pre-book Trains?

It is cheaper to book reserved tickets ahead at www.trenitalia.com, but not necessary. These fast trains rarely sell out. If the cheapest class does sell out, then the next upgrade can be just €10 more. So there's no "best," just different priorities of price versus flexibility. Ticket machines in the train stations are pretty easy to use, some taking cash as well as credit cards, and cash is more reliable.

If you can commit to a specific date and time for your train journey then yes, pre-booking can save you some money. Personally if I will always book ahead and grab the super cheap fares. Sometimes I even upgrade to 1st class if I can get the super cheap fare.

Booking (reserving a seat) is not a separate process. When you buy a ticket (either ahead of time on the Internet or at the station), if the train requires a reservation this is included in the ticket, and the ticket says date, train, coach number and seat number on it.
It is cheaper to buy the ticket ahead of time, but plenty of Italians just buy them on the day at the station.
Milan to Venice, the cheapest advance purchase fare is €22, tickets bought on the day cost €44.

"Regionalle" trains (local trains) do not require a reservation. Here there is no discount for advance purchase, you buy a ticket and it is valid on any train, But you must stamp ("validate") the ticket before you get on the train to stop you using it twice.

The only time you need to buy a reservation separately is if you have a rail pass.

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On the Milan to Venice route, the majority (if not all) trains are high speed. As the others have mentioned, you can easily book tickets online up to 120 days in advance at a considerable discount. However, you MUST be willing to commit to a specific departure as the compulsory seat reservations are specific to train, date and departure time, so the tickets can ONLY be used on the one train listed on the ticket, so there's no flexibility with that approach. Also note that the cheapest Super Economy tickets are non-refundable and non-changeable once booked, so be sure before hitting the "Buy" button.

If you'd rather have more flexibility with the departure day and time, you can easily buy tickets at the station the day prior to travel but you'll likely be paying Base fare which is the highest pricing tier. That approach will provide more flexibility but the tickets you buy will still be for a specific train, date and departure time.

If you buy locally, the Kiosks are very easy (especially as the ticket office at Milano Centrale often has a long queue). If you wish to buy onine, I'd suggest www.captaintrain.com which is a very user friendly website.

One other point to mention is that Italo Treno also operates high speed service on the Milan to Venice route, although in some cases they use a different departure station in Milan. Both Trenitalia and Italo use Venezia Santa Lucia in Venice.

Milano to Venezia super economy fares start at €9.