3 good games I would recommend are:
Wii Sports (should come with the console when you purchase it, always fun at party's)
Mario Kart Wii (a great multiplayer racing game that also has online play, meaning you can play people around the world)
Super Mario Galaxy (single player, and MAY be slightly challenging, though I can not describe how amazing the graphics are, and it is countless hours of fun)
One problem is that none of these games are shooting games. As the first answerer said, Lego is a good way to go. It's not "graphically violent", though it still brings the excitement to a 6 year old with the action and adventure they enjoy. Star Wars, Batman, and Indiana Jones are Lego titles on the Wii. That may be the way you would like to go for this Christmas. Mario games are always another option as well.
Overall my suggestion is Mario Kart Wii, because it is multiplayer, and you control the kart with a steering wheel. Though this is just my opinion, and your son(s) may prefer a shooting game like you said. Good Luck finding the games!
