My husband and I just recently visited most of these places and we used the train whenever possible. I highly advise purchasing tickets ahead because it keeps you on schedule and saves you so much time because American credit cards do not always work in ticket machines at train stations and the lines to use "real people" can be long.
I liked the website Petrabax, as recommended by Rick Steves. Very competitive rates (much better than Rail Europe) and they are available to answer any questions if you call or e-mail.)
They will then send you an e-ticket that doesn't have to be validated. Present at the station before boarding. Also, you then have a reserved seat at no additional charge.