I tend to take short hops on trains, so most of my Italian tickets were on regionale and I just bought them once I got to Italy. It is the case, however, that ticket lines at Italian rail stations can move very, very slowly. I assume part of the problem is that a lot of the people at the staffed counters are making tricky purchases (international tickets for a family, for example). Using a vending machine is a good idea. If for some reason you cannot do that, allow plenty of time to buy your ticket; otherwise, your train may depart while you're still in the ticket line.
You can check to see whether any of your trips will offer savings for purchase in advance by going to trenitalia.com and looking up each one. You'll need to use the Italian city/station names:
Roma (Tutte Le Stazioni), Firenze (Tutte Le Stazioni), Milano (Tutte Le Stazioni), Venezia (Tutte Le Stazioni), Padova and Napoli (Tutte Le Stazioni). If your Lake Como destination is Varenna, the station will be Varenna-Esino. Be sure to use the correct day of the week when you look up the schedule. Any train called "Frecciaxxxxxx" requires reservations (as do EuroCity trains, and there may be a few others), and the fare will tend to increase as you get closer to the travel date. From Venice to Padova you will have a choice between Frecce and regionale. The Frecce will generally save you only 12 minutes but will cost about 15 euros more if you buy the ticket at the last minute.
Edited to add: As Frank points out below, my wording was careless. What I meant was that if you wait to buy tickets on one of the fast trains, you will likely pay more. Other passengers may have long-since snapped up the limited number of cheap tickets that were initially available.