Seconding Raldo's post. The main scenario quests (ones with the flaming circle around the quest icon) and your class quests are the important ones, along with a few others that have the plus sign by the quest icon to indicate they unlock game features. There's still going to be some rather basic fetch quests within the main story, but they're intermixed with more exciting stuff, and just the fact that they are part of a story helps to keep them interesting.

The plain sidequests you can skip (or hold off on them until you're leveling other classes). That should eliminate a lot of the running around town stuff you get in the early few levels.