There are so many games on the market now what we did when we 1st got our wii was join game frenzy it's charges you every month to borrow the games they are posted to your house and it's free returns, Once we found a game we liked we bought it 2nd hand from ebay what we saved on the games we used to pay for next months fee to try some more. As far as i can remember there isn't a min contract either so you can cancel as and when.
There are plenty of family friendly games out there such as
Super Mario Galaxy(A great Platformer suitable for all)
Lego Star Wars/Indiana Jones/Batman(All brilliant)
Mario Kart Wii(Superb fun and the Wii Wheel is fun to use)