Endgame Confusion: What to do, what to skip?

[Taika]

Like Dement said, it's worthwile to do some "extra" content to help you later with the current ones. At levels 50 and 60, it's a good idea to do all the dungeons and (at least non-extreme) trials to unlock all the roulettes for tome bonuses. As also mentioned, the Crystal Tower 24-person raids are still somewhat relevant (because of the current relic quest) and worth doing at some point, and they're available at level 50.

At level 60 you can follow this list of Heavensward content from level 60 onwards. Your main priority at level 60 should be capping your allagan tomestones of lore each week (450 per week, used to buy i230 gear which can be upgraded to i240) and doing your weekly Weeping City for loot (i230, limited to one item per week, running Weeping City and Void Ark will also provide you items to trade for gear upgrade items and grade V materia). (Upgraded) Lore gear and Weeping City gear are the best gear you can currently have in the game without doing Midas Savage, and if you wish to do Savage, they're practically a requirement for that. The most important level 60 content to complete are the dungeons, Alexander normal, and the older level 60 24-person raid Void Ark.

At level 60 you can also start your relic weapon quest. Completing the first easy steps will give you an item level 200 weapon which is a good start for other level 60 content. If you wish to go through tons of grinding, completing the latest relic step will give you an item level 240 weapon which is the second best weapon currently in game. Alternative level 60 weapons are i230 Lore weapon (can't currently be upgraded without doing Savage), upgraded Esoteric weapon (i210), or Nidhogg extreme weapon (i235, but you need a good weapon and gear set to be able to beat the fight).

My reply is from a gear and progression centric perspective, but if you want to get into raiding, these are the things that are most important. Other stuff such as beastmen tribes you can of course do and they might be useful (for example the beastmen quest provide you free materia and / or useful currency for the relic quest).