Glad your interested in a wii its always good to see new fans. Wow theres a lot out there for multiplayer it depends do you want online or just multiplayer to play with friends or family? If you want both Mario Kart wii is a good choice, they got loads of them at walmart for xmas or you can get it discounted online. Great online single player and local multi.
If your a shooter fan I recommend COD WAW and MWR both great games with singleplayer and online.
However theres so much you gotta tell me your interests more specifically lol.