Train from Paris to Amsterdam

Amsterdam-Berlin is operated by DB. Book at www.bahn.de

The Thalys is indeed the train to take from Paris to Amsterdam. It is effectively the only connection.
From Amsterdam to Berlin you take the Intercity which runs every two hours.
Buy those tickets from the railway companies who run these trains (Thalys and Deutsche Bahn) or from an agent such as Trainline or Loco2, which asks exactly the same prices. These trips don't have to be more expensive than EUR 35 resp. EUR 39,90 when bought well in advance.

The Thalys, for sure. And tonfromleiden is right; if you order your tickets as early as possible, they are amazingly inexpensive. Our first high speed train ever was the Thalys out of Paris, and it was a great experience.

Thanks everyone for the advice!

High speed because you are in a hurry? The local lines are an experience with locals eating liverwurst on rye as you go through Germany, etc., and real scenes out the window rather than a blur of potato fields.

Laurel, you have a point. When we lived in Poland we used to take the trains, and what an experience! Talk about your back doors! We have a couple of funny stories, mostly involving my DH being offered alcohol or certain food items.... Which required a good slug of alcohol to get down.