You can buy through-fares for each part of your trip. You can decide whether you want to buy it via Interent or at the ticket office. If you buy your tickets at a ticket office, you can in most instances buy all ticket at the same ticket offfice. However to buy it directly from the ticket office is mostly more expensive, than to buy it via Internet (especially since, you can not get any saver tickets.)
To look for specific trains, I would recommend www.bahn.de. At least the schedule of all trains, can be found there (be careful, if you travel after 12.12.09 you have to wait for around half a month, because the new schedule isn't loaded.). If you know what you want, you should compare the prices of the different train companies (even for the same train you can easily find a difference of 20-30 Euros, depending where you buy the tickets).
However, some mentioned problems, when buying european train tickets with an american credit card.
cheers
757DUD

PS: For your question, regarding whether a Eurail pass, or individual tickets are better, the answer depends on the following question
1. Do you want to stay flexible and change your itinerary on short notice? --> take the eurail pass
2. Do you want to save money and are willing to invest some time searching for special fares? --> buy individual tickets