Don't take the train. Americans seem to think traveling to Europe you just jump on a train and boom you have cheap access to Europe, and beautiful scenery along the way.
Truth is trains are crap for long travel, they're expensive for anything other than short travel, like Amsterdam to Rotterdam etc. Once you start going longer distance, like Amsterdam to Frankfurt on the ICE trains, you're getting to the price point where it's the exact same as flying and longer travel times. From there is just gets worse with time invested in traveling on the train. I wouldn't take a train on anything lasting more than 4 hours of traveling time. Then on top of that, the whole scenery thing is crap unless it's a specific train that's labeled as scenic. Otherwise you're just going to be plowing through empty fields and maybe some rolling hills. It's boring as hell.
Basically the only positive about a train is easily accessible, but that's not always the case either. Especially if you miss a transfer or miss a stop etc and then you're stuck in a random train station in which you'll most likely get shit for help from anyone. Google Maps is great for trains, but then they're not always up to date with station closures or additional transfer buses. In the end the train is a bitch.
Fly that shit.