for a simple shooter you can't beat Lego Star Wars. i'm looking forward to getting Lego Indiana Jones
Metroid Prime 3 and the Wii Zelda are awesome games, but involves more than just shooting.
for a collection of decent mini-games with some shooters try Rayman Raving Rabbids. stay away from Rayman Raving Rabbids 2 it's a bit stinky...
Mario Kart is indeed a great game.. Much better than Mario Strikers, which is overstuffed with power-ups and items you have to unlock.
At the moment I'm also playing Bully, created by the same people who do the Grand Theft Auto games. Decent game so far..
Don't forget that you can also play gamecube titles on the wii, so there will be bargains in the used market for those games.