Ron, don't buy the railpass just because you get the tickets you need in advance. You'll really pay lots more for the convenience. In Italy, and on the runs you show, you will pay an additional 18Euro seat reservation fee for each Eurostar-category train you board. And, all of your runs above will most likely be on Eurostars. It tells you that on the Raileurope site but you have to dig a bit for it.
Next, you can buy the P2P tickets you need without a railpass on both www.raileurope.com or www.italiarail.com. It's a bit more expensive as both are ticket brokers but you will have your tickets in hand. My biggest suggestion is to not buy tickets a firm ticket on a Eurostar if the train trip is within 5 hours of your plane arrival. If your plane is delayed, your ticket could be toast.
Now the best advice. Buy the tickets when you get there. These trains don't fill up. As a North American, you just may not be used to seeing a passenger train or a train station. The Rome train station is massive and has at least 24 tracks deadheadding into the station. You will be shocked, stunned and amazed at how frequently trains arrive and depart. Plus, the metro is below. 55 trains a day leave Rome for Florence (where you will stop on your way to Venice). Each train holds more people than a 747. Don't fear the train stations or the train system. It's part of the local culture.
Finally, the P2P ticket costs. Rome/Venice 56.10Euro on the Eurostar. Venice/Vernazza 45.90Euro. Vernazza/Rome 33.70Euro. Are we near the cost of a railpass + 54Euro yet? I suggest you buy the P2P tickts only to save money.