Quests are assignments that are given to the player, usually by a Non-Playing Character (NPCs). An exclaimation mark appears above the NPC.
Some quests appear above the player character (exclamation mark). These self-given quests are the player's natural next act in the story.
Quests are colored according to their type. Each type gives different rewards.
MS2 players usually do the quests in this order because according to the value of the rewards.
You can choose to do them in any order regardless.