Do we purchase Italian train tickets in advance online?

Do you know which train station you need to leave from? Since you are this late in asking, I would wait till you are there since you probably have missed any discount opportunity. Second, the trenitalia site has historically not liked American credit card so you most likely could not had made an advance purchase anyway. Recently some have report success using a verified card. Third, a two hour window might not be enough time. The bus to the Central Train station takes at least an hour. Recently train service to Central has been opened but don't know the schedule or time.

I assume that you are flying into Malpensa. At the Malpensa train station, you can buy your tickets to the CT. Don't worry about missing trains. The train from Malpensa to Milan Centrale runs twice an hour. You won't have trouble catching the train. Next, I would suggest caution in trying to lock in tickets soon after you arrive in Malpensa. If your train requires seat reservations and your plane is late, you have to go through the hassle of changing your tickets to a later train. It's best to clear customs, walk to the train station and then buy your tickets to the CT. The agent will do everything. What time does your plane land? I can provide a link that shows the different runs to the CT after you land. It would be nice to get one that doesn't require an additional train change in Genoa. You can see these runs on www.trenitalia.com but you most likely cannot purchase as Trenitalia's bank doesn't seem to like U.S. credit cards.

Most trains in Italy you need to validate your train ticket before getting on train or can be fined quite a bit. Check this out when you buy ticket.

Thanks for your respnses, all! Larry, we're actually flying into LIN. It appears that there are no trains from that airport, so we would have to take a bus (or taxi) to Milano Centrale. It appears to be a 20 minute journey. It sounds as if we are best off waiting until we get to Milano Centrale before purchasing tickets. If anyone disagrees, please let me know. Also, below is information about the bus from LIN to Milano Centrale, taken from http://www.sea-aeroportimilano.it/en/linate/index.phtml?mod=per_mi_scroll&to=come_arrivare if anyone needs the info. Departure from: Arrivals floor Timetable: from 6.15 a.m. to 10.45 p.m. Every day, every 30 minutes Tickets can be bought at Agenzia Autostradale Linate or on the bus
Remarks: The bus also stops at Lambrate

Jim, To answer your first question, I'd suggest purchasing tickets when you arrive in Italy. When will this trip be taking place? Using the Linate Bus is probably the best option for getting to Milano Centrale from the airport, based on the information in your last post. When you arrive at the station, be prepared as it's somewhat "chaotic". Be sure to wear a Money Belt and watch your luggage! You can purchase your tickets either from the automated Kiosks (credit card required - AFAIK they haven't converted to "chip & PIN" cards yet) or from the staffed ticket office which is two floors down via "moving sidewalk". There's usually quite a long queue at the ticket office, but as I recall the Kiosks next to the office will accept Euro's as well. You may want to research the rail departure times for the day you'll arrive using the Trenitalia website, so that you have some idea on the times. If you don't make the train you're planning, there will be another along in an hour or so. There will probably be at least one change in either La Spezia or Genova Piazza Principe. The WC's are one floor down via the same "moving sidewalk", but these are "pay per use" so it's a good idea to have a few Euro coins at hand if possible. Happy travels!

Ken, Thanks very much for your response. We're not going until June, but I feel much better about what to expect.
Thanks to all!