Train tickets.

Danielle, A technique I often use (especially in Italy) is to buy tickets for the outgoing journey when I arrive in each town, which is usually several days in advance of the trip. Trains don't often "sell out" and even if that was the case, there's usually another train along in an hour or so. It's highly doubtful that trains would sell-out on the routes that you mentioned, as they're mostly Regionale trains. The Mini Fares are new since my trip last year, so I haven't had occasion to try them yet (but will later this year). Even with these new discounted fares, I still wouldn't bother buying tickets in advance. One disadvantage with that approach is that it "locks" the traveller into using a particular train at a set departure time. If plans change or they miss the train, that creates problems (which I don't like to have when on holiday). Happy travels!

It depends on where in Europe you will be using trains, and which kind of trains you will be using. All of the high-speed trains use airline style pricing, the sooner you purchase our ticket the cheaper it will be; the savings can be significant. For a lot of regular inter-city and commuter trains, advance reservations aren't possible all you have to do is purchase tickets at the station on the day of your journey. Which countries will you be traveling through?

Venice to cinque terre and then cinque terre to rome.

For Italy, buy when you are in country, but buy as many days in advance as your plans will allow to take advantage of the "mini fare" discounts. They are, as I understand it, not always available, but to get one you have to buy at least before midnight the night prior.

Mini fares sell out---there are a limited number of seats available. so you cannot count on getting them by booking a day or even several days ahead, especially on popular routes. The savings are so significant that it may be worth buying in advance even if it means using your credit card and paying the foreign transaction fee. It is worth at least checking the prices. If you cannot get the transaction to go through on Trenitalia, try BootsnAll, which sells Trenitalia tickets and passes on the mini discounts, but adds a $5 handling fee per ticket.