Danielle, we only used a saver pass for our first trip to Europe. I don't regret it, as it was one less thing to think about and gave us leeway in case we had miscalculated something (ensured we wouldn't miss a pre-purchased train, and would only be out any mandatory reservation fee). But even on the first trip I realized how much we overpaid for that sense of security, and by the end of the trip I was more than comfortable with navigating European trains in Germany and Italy.
For all trips since, we've prepurchased tickets that have a sizeable discount and that we're sure we will be able to meet the schedule. For the short runs or when we aren't so sure of timing or whether we'll want to linger, we just buy at the station.
As the others have alluded to, though, as you're looking at the timetables to figure out the cost of the trains, don't forget to keep track of the amount of transit time. (E.g., by the time you get to the station in Paris, find your train to Zurich, the length of the actual train journey, how much time will be left in Zurich, etc.) It really does add up.
Even though some of these are shorter trips, a journey usually eats up about half a day, and with 10 days and 6 cities, that's little more than a day left in some of the major cities of the world.
In the end, you know what you want to accomplish, but I would want to make sure you see cities, and not just whizzing-by countryside. :>)