Good LOZ for someone new to the series

Okay, I haven't played every Zelda game either, but I'd recommend either Ocarina of Time, or Link between Worlds.

Link between Worlds is basically a remake of Link to the Past. It's the first Zelda game I played, and it got me into the series. I think it really shows what kind of game the Zelda series is.
Ocarina of Time is an overall genius game (it's considered by some to be the best game ever, but that might be a little too much). The big difference is: Ocarina of Time is a 3D platformer, Link between Worlds is from a top-down perspective. They're both great, but different.

Plus, both of them are available on the 3DS

 

I would recommend Ocarina of Time for a first LoZ game of a beginner. Nuff said.

 

Honestly I'd try wind waker. Its a little easier than Ocarina and its good game, my second LoZ game and my favorite. Skyward sword isn't bad either, its what I really started with and i like it. Kinda depends on what system you have too

 

Depends on what system you have. If you have a N64 or 3DS you should play Ocarina of Time first (though original N64 version is the best one, imo. gotta stick with the classics, you know?).

Then maybe Twilight Princess for the Wii, Wind Waker for the Gamecube, Spirit Tracks for the DS, and A Link Between Worlds for the 3DS.

Ocarina of Time and Majora's Mask are available on the VC for the Wii.

 

I agree with the suggestions from everyone above and I would just like to add that, the 2-D Zelda games, like A Link to the Past, are more puzzle driven than the 3-D ones, like Skyward Sword. Not to say that the 3-D ones don't have puzzles they still do it's just more so in the 2-D ones

 

I'd say to either play Ocarina of Time or Twilight Princess.