I echo all of the stuff about the Wii, their down right fun and the games are much more focused on game play versus graphics or depth. But also keep in mind their still rather tough to find.
The 360 is just an awesome system overall. They have a lot more variety then just FPS as well. Including the best console driving game to date, Forza2. If any of your children dream of being a professional driver, I strongly recommend the 360, Forza (and probably Nascar 07 though it's extremely hard), and the FF Wheel. The other side of the 360 is XBox Live which is just a great network and tool. Lots of fresh content is released for old games for download, you can network with Friends, play head to head or in mass groups in most games, and download lots of demos/arcade games/movies/etc..
Good luck and Enjoy!
Edit: I voted for the Wii since you stated your primary focus was fun with the family.
Edit 2: Based on many long winded threads, I might head warning to Hylander and say try the pc for racing simulators as well.