Of course not! If you want to start though as Froggie said there's lots of choices. You could go 2D, 3D, Handheld, and each will give you a number of options.

In my experience people fall into two camps, the ones that prefer more Majora Mask, A Link to the Past, Wind Waker kind of more sort of story-driven, the people who prefer the kind of Twilight Princess, NES Zelda, and the more just "open ended" Zelda type games.

I'd actually say Zelda U would be a perfectly good intro game to the series but if you don't want to spend that money for it all I think the Ocarina 3D remake is also pretty good on 3DS.

For older games, I would say just don't start with Zelda 2 (Adventure of Link) which is regarded as sort of a black sheep. Zelda 1 and 3 (Original and A Link to the Past) give you a pretty good introduction to the series.