Fastest Way to Level: Questing or Grinding?

Personally, I find questing to be much more fulfilling. It also appears to be the quickest way to level a character as opposed to grinding. Questing also gets me involved in the story of World of Warcraft. I also find it easier to get in a group if I let them know I'm looking to do quests. Very few groups form on the premise of "getting together to wander around and kill stuff." Just about every group wants to run certain quests. Besides, if all I wanted to do was run around and kill stuff, I could play Counterstrike.....and it's free.

The trick for leveling quickly with quests is to complete the right ones at the right time. Do you need to complete all of the quests in the game? My experience tells me no. There are certain quests that can be skipped because of the time involved and the amount of travel to complete them. Since this is about Alliance leveling, I'll see if I can point out a few early ones along the way that can help out those getting started.