I'm a new convert to White Wolf as well, having just started a Hunter: The Vigil game. Hunter is wonderful, its really a toolbox game. The game is split into three tiers - I'm running Tier 1. This is pretty much early Supernatural. Some guys that know about the supernatural being and a trunk full of shotguns. Tier two you have more organization, and tier 3 gets weird superpowers. So you can do Supernatural, X-Files, Constantine, or Men in Black, as your tastes dictate.
The theme of Hunter is the candle in the darkness. Being a hunter is hard. You don't get paid to stake vamps and exorcise ghosts, you have to balance it with real life. You end up with all kinds of nasty things on your tail. That vamp you drug into the sunlight might have had a mate, and she'll stalk you back home. And there's the mental toll - the constant violence a Hunter partakes in can have a serious mental toll. Beware hunting monsters, lest you become a monster yourself. A fair number of serial killers in World of Darkness started out as Hunters.
There's a lot of 'blue books' that work great with Hunter as well. The Armory gives you all kinds of guns, weapons and gear to work with. Books like Mysterious Places, Urban Legends, and Midnight Roads are meant for any game, but work great with Hunter.
I also have Vampire and Geist, though I've not read/played either one. Having played oWoD the new one seems to fix a lot of the mechanical problems. The theme of vampire is desperation - what will you do to survive? You get to live forever, you get superpowers, but you have to drink people's blood to do it. And if you ever stop hating yourself you will become a total monster.
Geist is a little more cheery. You're a person who had a near-death experience. Actually, it would have been just a death experience, but a powerful spirit made you an offer you couldn't refuse. It returned you to life, but you had to take it with you. Now this spirit is fused with you. It is obsessed with the way it died and urges you to do things in that vein - the geist of a burn victim might urge you to start fires. But you get power over the dead and death, and are nearly immortal yourself. So long as you aren't too out of tune with it, if you do die the geist will just bring you back again. Having had a near death experience and being constantly reminded of death, most Sin-Eaters enjoy life as much as possible.
And then there's Exalted, the fantasy game. Best way I've heard it is to think about the Lord of the Rings movies. Aragorn, Gimli, and the Hobbits were playing D&D. Legolas was playing Exalted.
The other lines are Werewolf, Changeling, Mage, and Promethean. There are quick-starts available free for all these games.