Welcome to the forums, Scottio. I think we can help ya. =)
I personally would recommend the Mario Kart bundle over the standard Wii with Wii Sports. Mario Kart is still a high priced game even when it's already used because it's so popular, so you'll save a bit by getting Mario Kart Wii with the bundle, and buying Wii Sports as a separate game. Wii Sports is probably dirt cheap by now.
I would imagine you've a family of four, so yes, you'll need four Wii Remotes if you wish to all play games together.
The Mario Kart steering wheels are completely unnecessary to the game, believe it or not. It's just a piece of plastic, an accessory that might make youngin's enjoy the game more. If your budget's being pushed, you could certainly buy two for just the little ones.
If you'll be buying four player games that do use the Nunchuk (Wii Sports Resort, for example), then it'd be a good idea to buy four Nunchuk.
I'm not too knowledgeable on family-friendly games admittedly, hahah. I'm sure someone else could recommend some good family games, of course.
The Motion Plus is used for even fewer games than the Nunchuk, and buying four can certainly crank up the total cost. I'd imagine the only two games you'd consider getting for the family that do use it, are Wii Sports Resort (a beefed up version of normal Wii Sports) and New Carnival Games. There're plenty of other entertaining games out there, so you might not want to spend so much extra just to play two games.
Hope this answered your questions clearly.