Just to add to this, you're going to be given a handful of quests once you hit level 120, some of which may require you to log out and log back in to trigger them (those that magically appear in the tracker sometimes do), but some may also require that you just progress far enough into the current storyline quest before any additional options open up. It does feel a bit fragmented, as you can open up zones like Nazjatar and Mechagon without having fully completed the first part of the War Campaign, while you're also given quests to find Magni in Silithus to work on your legendary cloak (requiring a lengthy questline to obtain the cloak). All of that can be going on at the same time, and it is likely going to feel very overwhelming.

I would guess that you'd probably want to focus on unlocking world quests, as well as obtaining and leveling your legendary cloak, but I haven't hit 120 since before 8.3, and so I'm not sure what exactly the game throws at you, or when it throws it at you, as I already had a bunch of stuff done before 8.3 was released. Not that telling you these things makes it any easier to discern which questline leads to what, and, at the moment, I certainly don't remember the names of any of them to assist with that.