When even Rick recommends against a rail pass, you know it's a bad deal.
There are two basic kinds of trains in Italy. The Regional (including the faster Regional Veloce) trains are unreserved. Think of these as a "city bus on wheels." You buy your ticket, validate it (or get a hefty fine) and get on any train on that route. If there are no seats, you stand. No reservations are possible. So, with a rail pass you could just hop on these at will. But, they are cheap, so a rail pass wastes money. Just buy these tickets in Italy (tickets for these trains bought online have more restrictions than those bought at stations).
The other faster trains (Intercity or IC, and the various "frecce" or "arrow" trains like the FrecciaArgento, FrecciaRossa, and FrecciaBianca) require reservations, specific to THAT train (e.g. if you have a reservation on the 9:10 AM from Rome to Florence, it's not good on the 9:20 AM train that day or the 9:10 on any other day). If you use a railpass, the reservations are an extra €3 for IC trains and €10 for Freccia trains - per train. But if you buy a ticket for one of these trains (advance or last minute, on line or at a station), the reservation is included in the price of the ticket. With the reservation, you get an assigned seat. Advance tickets can be as low as €9 on short segments and even the long journey of Venice to Naples is €59 - far cheaper than any pass.
The catch is that the cheapest tickets (Super-Economy) are non-refundable and non-exchangeable - for any reason. The next cheapest tickets (Economy) are not refundable, but you can exchange them before travel and not lose the value. And full price (Base) fare tickets are fully exchangeable and refundable, so there's no advantage in buying them ahead.
Base fares in Italy aren't that high (that Venice to Naples trip, the longest a typical tourist might take, is €119; Rome to Florence is €44). if you can handle base fares, you can just buy at the station; if you want to save money and can handle being locked into specific trains, buy in advance. Note that you can buy domestic Italian tickets at any station in the country. For instance, you don't have to wait until you're in Orvieto to buy the Orvieto to Rome ticket, but can get it anytime you're in a station. If you're using a machine, it will default to departing from that station; just be sure to change it.
As for being shut out: on Regional trains, as I said above, this is not possible. On faster trains, this is theoretically possible, but most routes have so many trains that it only happens on very busy holidays. And a pass doesn't change these facts - you still need a reservation for the fast trains, and don't get any priority for them with your pass, so if you were really worried about a particular train, you'd have to book it in advance anyway. At that point, you can book the ticket itself just as easily.
Trenitalia is the operator of most trains in Italy. On main routes they have a competitor Italo. You can check both to see who has the lowest fares for your travel dates. Rail Europe does not operate any trains, does not show all trains, and often marks up the tickets it does sell (sometimes substantially). Unless you have a very specific reason to use it, avoid it.
When looking for train routes and prices on Trenitalia, use the Italian names of the main stations for each city:
Milan: Milano Centrale
Varenna: Varenna-Esino
Venice: Venezia Santa Lucia or Venezia S.L.
Florence: Firenze Santa Maria Novella or Firenze S.M.N.
Rome: Roma Termini