The Motion Plus is an optional accessory that improves on the motion-tracking capabilities of the Wii. Supposedly, some games require them, but the only one I've actually heard of hasn't been released yet.
In order for two people to play at a time, you will indeed need two Wii Remotes and two Nunchuks for the games that require them. You may also want to look into buying two Classic Controllers. The Wii has the ability to actually download games that were released on previous systems, and the Classic Controller is the most widely used controller on these games.
I have no idea about the dancing game, but Mario Kart is a good game for all Wii owners. It used to come bundled with a Wii Wheel, which was an accessory in the shape of a steering wheel that you could insert the Wii Remote into to improve on gameplay. It's entirely optional if you want to get that.