Topic: Controllers for Wii games on Wii U Virtual Console

I have zero idea where to find the information I am looking for, so I came here.
Here's the deal. My son got a Wii U for Christmas and is really digging the Virtual Console. He's all about all things Mario.
We have been waiting for Super Mario 64 to come out for the Wii U Virtual Console supposedly this year, but he's an impatient 9 year old boy, so he decided he wanted to just use the last off his Club Nintendo coins to buy SM64 for Wii and since there is virtually a Wii console in the Wii U, Wii Menu, we have Wiimotes and everything I was going to do it, but then I started looking at the controllers and saw that it says you must have a Wii Classic Pro Controller to play it and then saw that it says the same thing for Paper Mario, but years ago his older brother had a Wii and had Paper Mario and played it with a Wiimote, SO, my question is...
Are the Wii games in the reward section of Club Nintendo NOT for download to the Wii U (because it appears they are), and
If they are, why on earth couldn't you use a Wiimote or Wiimotion (Wii have both) to play the game?
And finally, I'm really really sorry for the placement, wording and general confusing nature of this question.
Thanks for your time!

You need to get a Wii Pro controller, make sure it's Wii not WiiU (as that will not work!)

You need a Wii classic controller, shown in the picture above to play N64 games on the Wii VC.
You can also get a Wii classic controller pro, shown below. Essentially the same controller, just with a re designed shape.

And yes, any game that is in the Wii shop can be downloaded in Wii mode on your WiiU.

Rats! Well, between Christmas and his Bday today I have dropped about $500 on games, controllers, adapters, cables, downloads, etc, and I'm just not buying another controller right now, so I guess we'll wait for SM64 to come out on the Wii U VC.
Appreciate y'alls quick replies. The info was super helpful! Peace!

Classic controllers actually go for dirt cheap if you can find them. If there's a gamestop near you that has it, for instance, I'd recommend picking it up, especially if you have a pro card and can get an extra $2 off and/or a coupon that applies to used accessories.