So I just wanted to bring all the information gathered here in one post:
First off, the quest item that you need to right click is sitting at the questgiver's feet.
Second, you can only choose ONE of the three spirits. Here are the benefits of each spirit.
Stag - Grants 10% increase with movement speed (does not stack with druid forms with increased speed, does stack with Darkflight and Nightstalker), Become friendly with all Stags in Darkshore (there are very few stags in the area now)
Moonstalker - Grants 10% increase in haste, Become friendly with all Moonstalker (cats) in the area (mainly in the southern area)
Bear - Grants 10% Damage reduction, Become friendly with all bears in the area (everywhere)
Third, bear in mind that once chosen that the buff will persist even after you level past this area, but only in Darkshore, and you will not get a second chance at choosing.
My Opinions:
If you want to level quickly, choose BEAR. You actually travel a lot in Darkshore by Nightsaber provided by the Nightsaber Riders. There are far more bears in the Darkshore than any other creature. Plus the less damage will help in case that involves getting hit by a large group of mobs.
If you ever foresee yourself need to gather herbs from this area, or fish... or whatever else you can do here.... and you really don't care about the buffs, STAG will by your best choice. While there are little stags in Darkshore itself the increased movement speed will help out when running around and gathering nearby herbs or dig sites.
If your a druid or you can care less about speed and armor, then MOONSTALKER is your choice. Haste increases all extremely important stats.
I will say this however: On PvP realms it should be noted that Horde may use Darkshore to get to Darnassus or as a refuge from a failed attempt on Darnassus. Thus making Moonstalker's effect a lot more wanting since it's usable at a higher level. Bear would also help in this case as well.
My choice, ironically, is Moonstalker. As a hunter on a PvP realm, that is high enough level to make this quest green, I really could care less about where mobs are. But the haste rating will help quickly killing my opponents. Every bit counts, and no one has confirmed that the Stag buff stacks with Aspect of the Cheetah.
Final note: Please don't vote mine down if you feel like it's repetitive (it's supposed to be just a place where to find ALL the information gathered) or if you disagree with what I'm saying, unless you feel that I am totally wrong about a mechanic of something. If that is the case please state why as a reply.