I would also recommend a link between worlds. It's a different style and it's pretty fun. 

Yeah, I'd recommend Link Between Worlds as well. It's a great game with elements of both classic "top-down" Zelda games and the newer 3D Zelda games. Though if you're intent on starting with a more typical third-person Zelda game, you could do worse than Ocarina.

Ocarina and Majora are good games to start with. Majora remains tied with Twilight Princess for my favorite Zelda game. I just wish I had a newer 3DS to play Link between Worlds =(

I've only played A Link to the Past and A Link Between Worlds. I don't know if there is a way to play the former on a 2DS, but if you can play the latter on it then I would recommend it. 

Start with Ocarina of Time, for sure.  On the 2DS you can then play Majora's Mask and A Link Between Worlds, in whatever order.

And then the original Legend of Zelda, and Zelda II, and Link's Awakening, and Oracle of Ages, and Oracle of Seasons.

Really you should play them all.  If you've got to cherry-pick, I'd go with Ocarina of Time for being the quintessential Zelda game and then either A Link Between Worlds or an Oracle game to experience what the 2D Zeldas have to offer, depending on your budget.

Of course, Majora's Mask is the best Zelda game, if not a particularly representative one.  And Oracle of Ages is, in my opinion, the best 2D Zelda game--though if you prefer combat to puzzles, go with Seasons instead.

I can't recommend A Link Between Worlds enough. Don't listen to anyone telling you to play Ocarina of Time, it's severely overrated.

E: Which isn't to say you shouldn't play it, but it shouldn't be the first that you play.

I would reccomend EVERY LOZ game to you. Except Zelda II.

I can't recommend A Link Between Worlds enough. Don't listen to anyone telling you to play Ocarina of Time, it's severely overrated.

 

E: Which isn't to say you shouldn't play it, but it shouldn't be the first that you play.

Yes, Ocarina of Time is overrated, but it's rated so high that it's still one of the best games out there.  A Link Between Worlds is indeed excellent, and would be an excellent introduction to Zelda, but I still think that Ocarina of Time will give you a better idea of what the series is about.

I thought a Link Between Worlds was fairly boring and substandard. I had a hard time getting involved in the game and I don't think I've finished it yet, actually. Whereas OoT, Wind Waker, and Majora's Mask all captivated me from beginning to end. Wind Waker remains my favourite, though obviously with the 2DS limitation, is not an option.

*quiet voice at the back* You should try Phantom Hourglass and Spirit Tracks...