[Shodo]

Thurg is definitely the easiest to start with. Join a faction "group" (often more like a mosh pit) in Wakening Lands at the entrance to Kael. This will raise your faction both with Thurg (for your quests) and with Claws of Veeshan (bonus for safe travel through Skyshrine/CS/etc). Alternatively you can just raise your faction while killing in Kael for the quest pieces, but that often isn't enough by itself since you need to get up to warmly (I think?) for the turn-in.

As for getting quest drops, Kael arena raids are the way to go, as Tupakk suggested. Paradox hosts open arena raids every few weeks or so if you want to get your feet wet - keep an eye out for one later this month [You must be logged in to view images. Log in or Register.]
Lots of mobs there can drop them, and you can definitely get them via soloing or grouping, but the mobs have a lot of HP and AC which makes the raiding method more desireable.