Help with working out long train trip, starting in Amsterdam, ending in France

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Hoping to get some help with nearly 3 weeks we have planned in Europe next January. We will be starting our train journey in Amsterdam and following the route listed below. Would like to hear of any alternatives and also if buying tickets at each train station ticket counter is the best paying option.
1. Amsterdam to Bruges
2. Bruges to Rothenburg ob der Tauber
3. Rothenburg to Munich
4. Munich to Innsbruck
5. This is the most difficult leg as we want to reach Carcassonne in France and there aren't any practical flying solutions. So we are thinking of dividing the trip up to Innsbruck to Montreux and then Montreux to Carcassonne. The Golden Rail has also been mentioned to us and sounds fantastic but seems to add a lot of time on to the journey. Is it a practical alternative.

Eurail passes are available (5 countries) and seem pretty expensive but not sure how they add up to p2p purchases on the routes we are taking.

Basically you have two possible options (both will be cheaper than Eurail Pass):
1) "Hunt" for discounted tickets for the most expensive parts of your route (Brugges to Rothenburg (start from 49 euro) and Innsbruck to France), if you travel in January you've got enough time to buy those online in advance. Plus you get "tricky" tickets for the rest of you journeys - Bavaria ticket for Rothenburg-Munich and partly for Munich-Innsbruck (till the border). Tickets within France and from Amsterdam to Brugges better to buy as well online and in advance.
2) Simply purchase regular international ticket for almost whole route (besides Rothenburg-Munich-Innsbruck part). Such international tickets issued with a help of TCV tariff work almost like a pass - valid for two month and allow unlimited stopovers on the route, plus can be bought any time - even 10 minutes before departure . For instance Brugge-Rothenburg ticket will cost app 90 euro. Innsbruck-Carcasonne app. 150 euro
So our suggestion - if you plan to stop a lot on your way from one place to another go with option #2, if you just want to travel between those place you mention directly without any stops go for #1 (since it will be cheaper)

Thanks for that information, I am going to print it out and see how I go "hunting". The only problem with pre purchasing tickets, is that I am not really sure of what the good and really good prices are...hmm.
I did want to mention that we may be changing that later leg of our journey. I have heard so many good things about the Golden Pass route and with tips from others, we thought this route may be a better option.
Rothenburg ob der Tauber to Munich (my wife wants to visit Dachau but if we can manage, might even skip Munich and go Roth-Dachau-Fuessen....trying to work out if that is too much in one day.
From Fuessen, we can head to Montreux, via the Golden Pass. We would probably transfer our Innsbruck stopover and ski time to somewhere along the Golden Pass like Mussen and then continue on to Montreux.
Montreux to Carcassonne....

Would this change any of the information you gave above? Thanks for taking the time to help, Europe train travel sounds geat but is complicated

The best thing to do about finding out best prices is to look for special offers like "Sparpreis"/Promo/Superpromo etc., mainly all the Railway companies in Europe got couple tariff stages - first they sell those promo tickets for less, afterward go for more expensive ones until it reaches regular tariff fare.
You can easily search for cheapest offers on the selected route really simply - try picking any dates from one to three month in advance and take a look at best offers at that date, then take a look at the other day etc. In such case after checking couple different dates you will exactly know the best offer available
Rothenburg, Dachau and Fussen all in Bavaria, so Bavaria ticket works for all those places - no need to worry here.
Golden pass route is pretty good, so go for it. Concerning tickets - you just need to mention your exact route while purchasing ticket (if it will be international ticket Innsbruck or Fussen-Zurich-Luzern-Interlaken etc.). If you will try purchasing discounted tickets like Europe-Spezial from Germany to Switzerland or Supersaver tickets for domestic Swiss travel just make sure you "connect" tickets to your timetable in order to avoid long stopovers and delays.