Good choice. The Wii kicks serious ass.
Yeah, getting a second controller set wouldn't hurt. I don't have any other accessories besides that. As far as I know, you don't really need anything else. Also keep in mind that a Gamecube controller is compatible with some games (such as Brawl, Goldeneye, etc). Stay away from the Wii Classic Controller.
The only games that I would say are ABSOLUTELY ESSENTIAL are Super Mario Galaxy, The Legend of Zelda: Twilight Princess, and Super Smash Bros Brawl. If you don't have those games, there's no point in owning a Wii.
If you really like Galaxy (which you will, it's a masterpiece) get the sequel, Super Mario Galaxy 2. Don't get the second one first, however. There's a bit of a learning curve and I'd say it's much harder than the first one. But it's definitely worth getting after you master the first one. In fact, it's even better. It's just important to go in order.
Other good games: Goldeneye 007, Sonic Colors, Mario Kart Wii (I hesitated to call this essential...I'd say it is, but others may not agree), Donkey Kong Country Returns, and, if you can deal with excessive kiddyness, Kirby's Epic Yarn.
Good luck!