EuroTrip Inquiry

Dear Friends,

Sights I expect to see on my train riding

As you know, next month we are embarking on EuroTrip 2012. We have flights and we have hotels. Woohoo! What we do not have is train tickets.

Are these a "buy online before we go" purchase or a "buy in the station when you get there" purchase? Which is easier? Which is cheaper?

If you suggest buying online in advance do you have a suggestion on which site to use? Which train to travel on (assuming that like airlines, there's more than one)?

If you suggest buying in the station, any tips? How long before the train departure should we arrive? Are there additional fees for buying the day of? Will I need a passport to buy tickets between countries or just to deboard when we arrive?

Other general train tips for Europe? While I've traveled by a myriad of transportation options in North America and Australia, the European norms escape me. But I am sure you, my very well traveled friends, have all the answers.

Much thanks for your help!