Confused about train tickets

The only reason to buy tickets in advance is to take advantage of discounts. But at three weeks you probably missed most of the discounts. You can look on Trenitalia.com to see what might be available. High speed and IC trains required a reservation at anytime so they can be purchased on line and sometimes at discount. BUT discount tickets come with restrictions and lock you into a schedule. If you can not get a discount then wait till you are there.

Regionale trains are open seating, no reservations, so those tickets are easy to purchase the day of travel or day before.

fs,

Given that there's only three weeks until your departure, you may have missed the opportunity for discounts on those trains where they're applicable. A few comments on each of the routes you'll be travelling.....

• Milan to Varenna - that's a Regionale, so buying tickets in advance can be difficult and there's no reason to do so as the price doesn't change. I'd suggest buying the tickets locally either on the day of travel or the day before, using either the Kiosks or the staffed ticket office (usually a LONG queue at the ticket office). Note that your destination station will be listed as Varenna-Esino. One important point to note is that you MUST validate Regionale tickets prior to boarding the train on the day of travel or risk hefty fines, which will be collected on the spot! If you buy the tickets the day prior to travel, DON'T validate them at that time as they have a "shelf life" once validated.
• Varenna to Venice - you'll need to travel back to Milan via Regionale and then connect with a Freccia high speed train to Venice. You may be able to save a few bucks by pre-purchase of the Freccia tickets, but note that those will be specific to a particular train, date and departure time and can ONLY be used on the one train listed on the ticket. If you board the wrong train, hefty fines. For the leg from Varenna to Milan, you could purchase those tickets at the same time as those for the trip to Varenna, but don't validate them until you use them. You can also buy tickets at the helpful Tivano Tours office in Varenna. Note that your destination station will be Venezia Santa Lucia.
• Venice to Florence - if there are still discounted tickets available, you may be able to save by pre-purchasing those. You'll be traveling on high speed train on that route, and you can use either Trenitalia or the newer Italo trains. Note that your destination station will be Firenze S.M. Novella.
• Florence to Vernazza - you'll likely be using a combination of both "premium" trains and Regionale with a couple of changes, depending on which departure you choose. Check the Trenitalia website for details.
• Vernazza to Rome - the quickest way to travel that route is to travel from Vernazza to La Spezia via Regionale, and then connect with one of the direct high speed trains to Rome. There are several of the direct departures each day, and I'd probably use the one at 10:04. Note that your destination station will be Roma Termini.

If you want to check to see if there are discounted tickets still available.....

http://www.trenitalia.com/

http://www.italiarail.com/ (reportedly the website is more "user friendly" than Trenitalia)

http://www.italotreno.it/EN/Pages/default.aspx (Italo doesn't operate as many routes as Trenitalia, and sometimes use different stations - you could use them on the Venice to Florence route).

For buying tickets, you may find it helpful to have a look at THIS video or the excellent Ron In Rome website. Be sure to check into the method for train changes.

If there are no discounted tickets available, it's just as easy to buy them locally a day or two before each trip. In that case, you'll be paying "Base Fare" whether pre-purchased or bought locally.

Buon Viaggio!

Thank you so much for your help. I've been online today and I think I can still snag some discounted tickets. It's all making a lot more sense to me now. You've been a tremendous help!