As Madras says, getting night trains with sleeper compartments is the best idea. You play an extra supplement, even with the interrail ticket. Its usually between 5 and 10 euros, which is considerably cheaper than anywhere you will be staying!
If you're going to all the famous western cities in peak times, I really wouldn't expect your holiday to be anything other than very expensive. Great fun, but very expensive. Hostels (even the poor ones) will all be over €20 a night, on the night. In amsterdam it can get seriously steep and into the €50's.
Take a sleeping bag and sleep on beaches, it's amazing and costs nothing!
Also, it's a lot cheaper to:
Get a package holiday to your furthest destination away. (package holidays are cheaper than the flights themselves)
Spend a week chillaxing and pissing about
Organise your inter-rail ticket to start the day after the first weeks holiday ends
You then have 4 weeks to travel in a straight line back to amsterdam (for the ferry back to NCL), which means you wont have to double back on yourself at any point, or visit anywhere twice/you don't want to.
Hey presto! 5 weeks holidays!
hope you enjoy it mate, best time of my life