You might find that your 6 and 4 year will be able to figure out that Wii U remote before you are able to. If you get the classic controllers, you will need the Wii remotes to make them work. They plug into them. Not all games use the classic controllers or are compatible. For example the dance games. The Wii remotes are not that difficult to get use to. You have elderly people using them in nursing homes that have never held a classic controller. Nor have they ever played a video game in their life.
Since you are interested in a Wii, I think the Wii U would be a good route to go. You would have access to the Wii games and the newer Wii U games. You need to keep in mind that the Wii will fade away as the Wii U takes its place. I will go out on a limb here and say that this is the last Christmas for the Wii.
The dance and sport games will mainly use the motion controls of the Wii controllers, which would involve swinging, or waggling the controllers around.
Whichever route you go, you will need to invest in the Wii controllers.
And it looks like you will need a Wii sensor bar to use the Wii controllers.