Oh right, I forgot that Majora's Mask took place after Ocarina. 

I would say there are 5 great Zelda games to play, Ocarina is a good starting point for the 3D series. Link tithe Past for the 2D series. All of the others I didn't find as good. The original Legend of Zelda is nearly unplayable, Adventure of Link is actually surprisingly interesting, but I would say for hardcore Zelda fans only. Wind Waker, Twilight Princess, and Skyward Sword are all fairly bloated and boring compared to other Zelda games.

Link to the Past > Link's Awakening > Link Between Worlds

Ocarina of Time > Majora's Mask

Excited for you think-man! Playing Ocarina for the first time is a special experience. It's still, in my mind, the best game of all time. Hope you enjoy it!

That being said, I might suggest starting with A Link to the Past if you can get it, because that game established many of the items, tropes, and mechanics that appear in later games. For me, it's the quintessential Zelda game.

Ocarina of Time for the 3DS is an excellent way to start the series man! After you are done with it you unlock a Master Quest on the 3DS version so you have a lot of content in the game. Easily, 40 hours+ of gameplay!

After that game you could try the 2D zelda games to see what is your favourite Zelda style. A Link to the Past is a great way to start.

Dont read the rest if all you want is this answer:  You can't go wrong with any mainline zelda game (3D or top down)

My favorites are top down zelda games thanks to amazing puzzles (also some of my all time fav games) so I would say the most popular one which is Link to the Past. My favorite is Oracle of Seasons though, absolutely brilliant game.

As for 3D Zelda games I'm prob not the right person to ask but I'd say Twilight Princess for Gamecube. I didnt care for Ocarina of Time or Skyward Sword. They were ok but not something that I would go back to any time soon. Wind Waker is good and beautiful.

So in order this is how I would rank them

Top Down(Just bought Link Between Worlds so no opinion on it yet)

1. Oracle of Seasons
2. The Minish Cap
3. Link to the Past 
4. The DS franchise (meh)

3D Zelda

1. Twilight Princess
2. Wind Waker
3. Ocarina of Time
4. Skyward Sword

If you just want to go with the most popular it would be Ocarina of Time and Link to the Past.  I think that is partially because of nostalgia though.

The early 2D zeldas haven't really stood the test of time. original zelda, Half the time you're just gonna be wondering where the hell to go and what to do.

Ocarina of Time is awesome, but my favorite is Wind Waker.

3DS ambassadors got it for free :D

OoT is considered like the "center" of the Zelda Universe, story-wise so it is a good place to start. It's also really good. The original would be the only other place to start really, but it doesn't have much of a story.

a link to the past is the best way to start ..and you should probably play ocarina first on n64 or GC on 3DS its the same game but you have a different feel while playing it its just not the same so you probably wont like it.

This series has a full rich story if you put them all together, not for separate. Also, OoT 3D is a good start. You can check also ALBW in the same platform. 2 different style Zeldas, both are good.

I recomend to left ALTTP maybe for the last. It is the one with most dungeons and if you like dungeons, it will be a pleasant surprise when you play it.