We just got one, so I guess I can sort of answer this one! The basic box comes with one remote and a num-chuck (iirc). If you want to play two person games, you need to get an extra remote - and for certain games, an extra num-chuck. Wii Sports comes with the basic set. Iirc, the boxing game on Wii Sports is the only one that uses the num-chuck.
We ended up getting the Wii Play set, which has the extra remote, and another group of games (a memory game, target practice, pool, air hockey, fishing, a racing game, and one or 2 more I can't remember). I'm not sure if I would consider it a must-have, but since it basically got us a bunch of games for another $10, we figured it post-poned needing to get more for a little bit. We also got another num-chuck.
Wii Sports has bowling, baseball, tennis, golf and boxing. Dd likes bowling the best so far. I like tennis best - probably because it is the sport I am the best at IRL, lol. (I suck at baseball, and haven't tried boxing yet.)
The kids also like making new avatars (Mii's) and messing around with them, lol.
Things we'd like to get - Wii Fit, Dance Dance Revolution (ok, that's the one I want). Ds really wants Mario Kart from playing it at a friend's house, but that is still very hard to find. Dh wants a better golf game, maybe the Tiger Woods one.
Oh, and supposedly soon they will be coming out with a personal trainer type game for the Wii Fit that does more than the basic one. Tho that's more for the grownups than the kids.