Lots of mixed advice and some consistent advice. The key take home is you won't need to play any Zelda games to be able to play the WiiU version, but as a gamer you deserve to give it a shot.
The Zelda games have varied quite alot through their history and so not all Zelda fans like all games. There are games that most like, games that many like and games that are polarising. On this point I have to disagree with Spemanig; while there is no guarantee that you will like them, both Ocarina of Time and A Link to the Past are the series' most acclaimed games so they would be my recommended starting point. Both games are playable on the WiiU i believe, even if that's not necessarily the best place to play them. (see S Peelman's post above)
I also enjoyed my replay of Windwaker in HD (WiiU retail) more than I enjoyed playing the game first time. It really is a beautiful game, but it's one of the polarising games mentioned above. Personally I didn't really care for Skyward Sword (WiiU via backwards compatibility), the only Zelda game I would say that about, but there are a number of people here that list it as their favourite.
I think the lengthy replies that many have provided are a pretty good testament to the quality of the series.
p.s. The WiiU controller is much more comfortable than it looks and is one of the reasons I preferred Windwaker on WiiU. The new game will undoubtedly support the pro controller too though as most games support off-TV play and off-TV play basically requires the game to be playable without any significant touchscreen/second screen features.
