The Wiimotes take 2 AA batteries each. Charging station kits replace those with a large single battery which can be removed and charged. Not necessary, but handy.
I've got four controllers and three nunchucks. And yeah, you won't need nunchucks as often as you think - but you will need them.
As more titles come out with it, you'll want the Motion Plus attachment for improved tracking. Wii Sports Resort comes pre-packaged with it, but if you start buying games which use it you'll want a Motion Plus attachment for a second player (or more).
The balance board is overrated, you need Wii-specific controllers for Guitar Hero and Rock Band, etc.
Oh, and buy one of those add-on packs with mini baseball bats, tennis rackets and golf clubs. Totally useful.