The only required content is the quest with the fireball icon (main story quest) because these unlock new areas and all of the optional content in them. They don't involve grinds (unless you consider doing the story a grind, which some people do if they don't follow the story).

The blue quests are recommended because they unlock things but are not required. Beast tribe quests are blue and you work your way up to the maximum rank to get a mount and other little things. The cosmetics they usually give are to dress up as that beast tribe but sometimes it's just gear for crafting and gathering.