I would actually go for the XBOX 360 Kinect. It uses motion capture (or something)...way more advanced than the Wii technology (which is what we used to have). The XBOX Kinect is more like you have Jedi powers... They have similar games as the Wii - sports ones where you run and jump and lots of other stuff, so you stay active. You can also play typical video games with it (just a video control) that doesn't require being active, for those times where you don't want to be so active.
We LOVE our Kinect. We are like you - limit it's usage. Actually they are only allowed to use it on the weekends. They homeschool, and I've found the video games are distracting to them. So, only on the weekends.
We can also live chat with people on our TV through it (video chatting). It's a lot of fun. I really would not buy a Wii unless you look into an XBOX Kinect first to make sure you don't want that instead. My hubby LOVED the Wii (same reasons you mentioned), and we bought a Kinect. It was on a great sale and we wanted some really good exercise games. We bought it and were blown away by it's technology in comparison. One of the exercise games we use (adults) it's actually puts us IN the game so we can watch ourselves. There is a personal trainer that helps you through it all and can even tell you when you're doing something wrong.
Anyway, enough of my rambling! Definitely look into the XBOX Kinect (there are different versions of the XBOX, so you want the Kinect one - it's the newest version).