What other bits and bobs would we need / want to go with it? We don't play any computer games, but I think some of the "moving about" Wii stuff sounds fun. I would need a Wii fit for that though, right?
Yes, you need one remote per person playing. A nunchuck plugs into the remote for additional gamplay, essential to some games. it has a joystick controller on it and is also used for things where you use both hands, eg boxing.
So, you need a Wii, two remotes, two nunchuks, Wii Fit board if you want to do yoga etc, plus any other games you fancy. Some games (like Wii Sports Resort) need a Wii Motion Plus attachment. That's also an extra cost. You should be able to find bundles that include more remotes etc.