Well, I would say, much like the others here, that it depends on your personal preferences.
If your looking for a shooter, the call of duty series is an excellent place to start. They're all pretty good, but I'd recommend modern warfare reflex, assuming you haven't played modern warfare on another console. There are also plenty of good rail shooters to choose from: in that realm I would go with either Deadspace: Extraction or one of the resident evil chronicles games.
For something a little lighter, maybe try boom blox: bash party. It's a really fun game with a relatively simple mechanic at its core. De blob is also a pretty fun game, it's very fun and colorful.
If what you want is something incredibly stylish, then I would probably go with No More Heroes, which is sort of like a Kill Bill movie translated into video game form. Madworld is much the same, but it's a little shorter, with more emphasis on getting a high score. If you don't want a lot of violence, though, go with Okami. It's incredibly pretty and very interesting. Plus it's very long but never really starts to wear on you.
If you love a good old adventure game, there's nothing better than Zack and Wiki: Quest For Barbaros' Treasure. The puzzles are incredibly well designed and mind bending. For something a little more interactive, though, Hit up Zelda: Twilight Princess; the visuals are gorgeous, the game-play is fun, and the plot is incredibly intriguing. You could also do Metroid Prime Trilogy for the same reasons.
Whatever you choose, have a good time, and I hope you love your Wii (I know I love mine)!