The Wii comes with a Wii Remote and a Nunchuck.
If you'll have multiple people playing games, consider getting more Wii Remotes.
As for additional Nunchucks, many games don't use them. Look at the games you'll be getting. Once you get a game that will require all players to have Nunchucks attached, then consider getting them. For example, in Wii Sports (which comes with the system), the only game requiring a Nunchuck is Boxing. This can be played by two players. Baseball, Golf, Tennis, and Bowling do not use the Nunchuck.
As for games, one of my all-time favorites on ANY system is Mario Kart Wii. It's fun for all ages, really. Every member of my family has picked it up frequently; the controls are very intuitive, so anyone can learn it fairly quickly and have fun with it.
Wii Play is another game that can be fun, so if you're getting another Wii Remote, might as well get one that comes with that game. The game adds $10 to the cost of the Wii Remote. It's a collection of fun little games.
Super Mario Galaxy is another fun one. There's actually a way for a second player to jump in and "guide" or "help" the first player in some ways. Point things out, stop enemies from moving, and so forth.