Reddit mentions of Nintendo Nunchuk Controller - Black

The game pad turns off when you switch to Wii mode.

You will need the Wii Remote Plus and Nunchuck to play the classic Wii games but, the classic Wii remote will work as well if you already own that. In addition, I'd also recommend grabbing a classic controller if you plan on playing Wii games like Super Smash Bros Brawl as the Wii U Pro Controller will not work.

There is an official forum list here of compatible external hard drives, but I haven't put much of a dent in mine yet so, you may want to hold off.

Typical file sizes for older SNES games seem to be in the 20-30 MB range.

All WiiU games and any Virtual Console games that are in the WiiU's eShop can be default be played 100% with the gamepad. If you want to play old Wii games you will most likely (99% of games) need a Wiimote and nunchuck. Based on personal preferences you can then opt for a Pro Controller to use with certain games if you want. For example, I played Hyrule Warriors exclusively with the Pro Controller even though I didn't have to, just 'cause.

It depends on what games you want to play.
The old school Wii Remote and Nunchuck will work on many multiplayer games and are also necessary for playing any Wii games

However, if you want to play Wii U games, you can also choose the Wii U Pro Controller. (which can NOT be used when playing original Wii games. Only for Wii U titles)

I have found that owning one of these isnt necessary, I have been able to get by with 4 players on my Wii U using only the supplied gamepad and 4 old Wii motes (nintendo land, mario kart, mario bros can all work with the old wii motes).

It's also probably worth mentioning that this is a Wii subreddit, and your question relates to a Wii U.
I don't mind one bit...but you know what people can be like :)

the old Wii remotes were upgraded towards the end of the life of the original Wii, so if you plan on getting Wii remotes, make sure you get the Wii Remote Plus models, to ensure you can use them on everything (some games require the added "Plus" functionality to work)

hahaa So confusing. Wow.

So would this be the right combination?
Wiimote: http://www.amazon.com/Nintendo-Wii-Remote-Plus-Black/dp/B00N4OAELY/ref=pd_sim_63_22?ie=UTF8&dpID=41pDVGqtA6L&dpSrc=sims&preST=_AC_UL160_SR160%2C160_&refRID=16YNA1JFTG39VX3J6MD2

Nunchuk: http://www.amazon.com/Nintendo-Nunchuk-Controller-Black-Wii-U/dp/B0094X1ZXU/ref=pd_bxgy_63_img_2?ie=UTF8&refRID=0QJQKGMFCCBYZ7H2P21M

Controller: http://www.amazon.com/Wii-Classic-Controller-Pro-Black-Nintendo/dp/B002TLTBN0/ref=sr_1_3?s=videogames&ie=UTF8&qid=1464291516&sr=1-3&keywords=Classic+Controller+Pro&refinements=p_89%3ANintendo

The Wiimote and Nunchuk say WiiU on the box, but the controller says Wii. Is this right?