I honestly don't think I can pick one, there are so many good ones!
The original LoZ is a good choice because you are just hurled into a world you are force to travel around with no hints. But I'd say this is more exploration than adventure.
In terms of "going off on an adventure" many Zelda games use this with perfection like Skyward Sword, the Wind Waker, Ocarina of Time, Twilight Princess, and A Link to the Past. They all do a superb job of creating a scenario in which Link must jump into a massive world for a bigger cause, and in all of these Link must leave his home.
Overall after contemplating for a long time i'd have to say the Wind Waker for a few reasons. 1. He is a child leaving his home to save his sister 2. He must sail in a tiny boat across a vast ocean without knowing whats in store and 3. You should all know that feeling you get when you are sailing and a tiny island speck is visible off in the distance and you have no clue what people or treachery awaits you once you land