I intended to write up this post with all the paperwork next to me, but me and my paperwork aren't in the same spot right now, so let's just see if I can do this off the top of my head.
If I understand everything correctly, it seems like there's not much that I can do before I get to Amsterdam in terms of telling them I want to live there. Because I'm American, I don't have to apply for an MVV (Machtiging voor Voorlopig Verblijf - authorisation for a temporary stay) before I get there. This is a huge difference between France and the Netherlands (in a good way!). When I moved to Paris, I had to apply for a long-stay visa while I was still in the states (which required three separate trips to the French consulate in Washington DC) and then basically repeat the entire process when I got to France. But in moving to the Netherlands, I get to skip this step altogether ... which is just bizarre and kind of wonderful. The only people who DON'T need the MVV are EU/EER nationals, Americans, New Zealanders, Australians, and of course anyone from Switzerland. My nationality also exempts me from having to take a TB test once I'm there, and again, that's something I had to do in Paris (and that chest X-ray cost a lot of money).
However, once I arrive in Amsterdam, I'll have to go to the City Hall in the municipality where I live and apply for a residence permit. This requires a ton of paperwork and a lot of money... between €330-430, depending on which permit I apply for. I know that sounds extreme, but when I think about how much I ended up paying altogether for my Paris visa and carte de sejour, it's actually about the same. The residence permit application gets sent off to the IND (Dutch Immigration and Naturalization Dpt), and they have six months to decide if they want to let me stay. And during that time period, I'm considered legal. This page explains everything rather simply, though the first place I learned about all this was the 30-page IND brochure, which gives a lot more details.
If I'm granted the residence permit, it will be good for one year, which I think is great. One year will be enough time for me to figure out if this whole Amsterdam thing is a good idea, and if everything is going well, I'll be able to extend the permit (the IND will send me an extension application three months before the first one expires).
I still have a huge amount to do (like save money) to prepare for this move, but it's all very manageable and just requires a lot of self-motivation. The hard stuff will happen once I'm there - like finding a place to live in one of the most most over-crowded cities in Europe. That may have scared me a few years ago, but after budget apartment-hunting in NYC (which was even more difficult than Paris) on two separate occasions, nothing can scare me. Even the prices in Amsterdam aren't a huge concern, and again, I have living in NYC and Paris to thank for that.