For anybody who's wondering, the officially confirmed LoZ timeline (at the present time) looks like this:
Ocarina of Time starts it out, and then, based on that game's ending, the timeline splits into two branches, one which contains Majora's Mask and Twilight Princess, and another which contains The Wind Waker and Phantom Hourglass.
There is quite fervent debate still about the placement of the other games in the franchise, although evidence has emerged that would concretely place the original Legend of Zelda and its direct sequel, The Adventure of Link (Zelda II) as well.
As for where the OP should start, the best game to play if you're just starting the series is, IMO, Ocarina of Time.