Hrm...well, as I remember there is no direct train from Salzburg to Lucerne, so you'll have to transfer at Zurich. It's not that bad of a train, in fact I barely remember it, but I did it in the morning. I don't think it is worth a night train.
As for other suggestions,...let spontaneity guide you in Prague, whereas have a good mapped out plan of what you want to do in Vienna. I found Prague to be very relaxing in terms of just wandering (albeit there were some very long walks in there...good for the soul) and Vienna to be more of a "sights" oriented town, where you have to know where you're going and at what time. Don't miss the Summer home of the Habsburgs in Vienna, very cool. Lucerne is so quiet, I found it hard to really spend more than an afternoon and a night there. Go walking as far off as you feel comfortable (preferably look back around to the river) and get a feel for what typical Swiss living is. For Salzburg, do the Monchberg cliff walk - very good views. I didn't do the Sound of Music thing there, but that could be fun as well. It's kind of a small town, but you can easily just wander around for a day and have fun.
Anyways, have a great trip and post reviews for everywhere you go!