Actually, which WW Storyteller game you get should depend on how much exposure you want to the World of Darkness.
Exalted's cool, very anime-like. And is completely stand-alone; while there are a number of highly obvious parallels/connections, it has no actual connection to the WoD.
I can't speak for Adventure!, though I'm told it uses the same Storyteller variant that Exalted does.
Of the pure WoD games (Vampire, Werewolf, Mage, Changeling, Wraith, Hunter, and maybe Demon (which I don't have)), it depends on what your goal is.
If you're brand new to the WoD, I recommend HIGHLY Hunter: The Reckoning. It's the first game to deal with the WoD as a whole (unlike the first five which focus on the title type's subculture), and provides a GREAT transition from the "crunchy" games (like 3E, Shadowrun, etc) to the "fluffy" (i.e. theme/story/character-based) games that are the bread and butter of the Storyteller system.
Mage is a *great* system, but the very things that make it so attractive are exactly what make it hard to run if you haven't had similar experience already.
The single best resource for these questions is the Ex Libris Nocturnis web site (
http://www.nocturnis.net).
BTW, IMO the games move away from "crunchy" in the following order: Werewolf, Hunter, Vampire, Changeling, Mage, Wraith.