After you do the story on one character you can basically avoid it all on every character after. All but the short bit at the beginning inside the Maw. You get to pick your covenant or choose to level through it as normal. If you choose the Threads of Fate (not following the story) you can go to each zone and get a story quest that's just a bar to fill. You fill it by just doing quests, including dailies or dungeons in the zone. It seems to replace the chaptered story quests in each zone. And you can start doing dailies to get your AR started early. You'll also be able to queue up for the four starting dungeons right away.
Also OT: Yeah it felt like a cheap knock of Pandaria but with Angels to appease the crotchety christian crowd.