Hello! We just got a Wii this summer. I have 3 kids 9,6 and 4. We like Wii Sports, which comes with the system. For family games, my favorite is Mario Kart. My 4-yr old daughter can play no problem, and it is a lot of fun. You do want to get the steering wheels, because it is much easier to play. We also like Mario Party 8. It's like a video board game, with mini-game challenges. I do have Wii Play, which came with the extra remote, but we hardly play that at all.
The next one we're dying to get is Rock Band 2 (complete set). We played a friend's on PS3 and loved it. But, my kids are a little older. Truthfully, my husband and I had the most fun with that one!
If you want to try out games, I recommend getting them used from Gamestop. They won't be much cheaper than new ($5), but they are guaranteed to work and you can return them if you don't like them. They give you 7 days, so enough time to see if you like it.
Have fun!