You DO want to get involved in Zelda if you have any interest in the Action-Adventure genre. It is to that genre what Mario is the the platformer and Dragon Quest/Final Fantasy is to the JRPG: Argubably the founder and high quality over a long period of time.
One thing to bear in mind though, is that the Zelda series is pretty big and diverse, even though it's mostly all within the same genre and type of setting.
If I were you, I'd play Link to the Past on the SNES or Wii Virtual console first. Ocarina of Time is best played on the N64 or especially the 3DS rather than the Virtual Console, and is arguably the place to start with the 3D games. LttP is probably the best 2D game, establishes a lot of the series conventions, and does a decent job setting the tone for the non-3D entries in the series.
DO NOT start with the DS Zelda games. They refer to the events of Wind Waker for the GameCube, are are considered to be among the worst canonical entries in the series by the masses. And I say that as somebody who thinks Phantom Hourglass is underrated.
The one thing about Zelda worth keeping in mind is what it's about: a mixture of combat, exploration, and puzzles. Some Zelda games do better in one area than others, but it's all about the three being mixed together to the extent where it's hard to tell where the boundaries between the three are. Zelda has had great stories since the 80's, but the series is NOT about the stories. It's about your personal adventure.







