Apparently it changes how multiplayer will work slightly so.. it's an important choice ! *spoilers just in case*
Way of White is the usual Demon's Souls system.
Sunbros are enhanced for helping people.
Princess Guard summons you ala Old Monk to protect her from people who try to kill her.
Crescent Moon makes you into a bounty hunter.
Forest Hunter makes the forest area into a Deathmatch, where you mustkill tresspassers.
Gravelord lets you summon NPC black phantoms into other people´s worlds.
Darkwraith is normal Black Phantom experience.
Path of Dragon makes you try to power yourself up by fighting other people from your covenant.
I'll probably go Crescent Moon since it's apparently the Chaotic Good covenant, and I always favored the Chaotic Good alignement.
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Best LPer ever, Gix ! : http://www.youtube.com/watch?v=Vt5YKmP7ecY