OOH, Sarah, you will love it!
If your work is paying for schooling, I can recommend the American School in The Hague as an option. They have brilliant sporting facilities, but it is by far the most expensive of your international schooling options AND the location is not the most convenient for living/working in Amsterdam or Delft.
The British Schools in Amsterdam and The Hague are also brilliant and are truly international. I have good friends at all three of these schools and I'm happy to put you in contact, send me a PM.
For housing, look at Funda.nl. 'Te Huur' is to rent, and you can see examples of prices and options. Delft, I suspect, will be much more affordable than Amsterdam, and has a lovely vibe, being a university town, and is out of the normal expat zones, but if you want to be in the middle of the bustle, Amsterdam could be more you. Amstelveen, where Heleen lives, is a good choice for the British School in Amsterdam, and for public transport (brilliant and clean and safe) and is brilliant for the airport, which makes a big difference when you arrive after long international flights! Schipol airport is efficient and clean and well serviced with fast trains and is one of the nicest you will encounter in Europe.
The Dutch are open and straightforward and the bike culture is fabulously egalitarian and social......I would even consider getting new bikes there as Dutch bikes are so comfortable, though expensive. And it is a strong cultural value in Holland to 'be normal' and not stand out. The Dutch don't wear helmets (except for children) so everyone will identify you as foriegn with yours (close your eyes and ears, Heleen!) but we stuck with wearing them and I am still firmly on Team Helmet.
It is well worth doing a cultural appreciation course when you arrive, the Koninglike Institute of Tropical Studies in Amsterdam does a brilliant one that will give your a two year headstart on navigating life and social customs in your new home!
So excited for you, you will love, love, love it, I am sure!!!! Now put on your orange shirt, paint the red white and blue stripes of the Dutch flag on your face, and shout "Hup, Holland!".
You will find the medical system very different to the US, it is efficient and fair but run very differently which foriegners, especially Americans in my experience, can take a while to get accustomed to. I was a fan, but not all my expat friends were....
Check out expatica.com for lots of good info and links.
Stay away from complainers and enjoy :).