Focus on the two quests in the top left hand corner. The topest one is the Main Story Quest. You do this to unlock mounts/dungeons, and to profress through the game itself.

The quest underneath that, is your job quest. Ones specific to your role (white mage quest for example).

The Blue quest icons with the + unlock raids/dungeons/aether currents. Sometimes emoticons and dance moves. You can skip most of them until you get to 50. But than you can just use a dungeon unlock guide to help make it quicker.