I’ve just started to play Destiny 2 on PS4 and wanted to share my spoiler free thoughts as I go.
In order to unlock the crucible so you can play online you need to stick with the single player campaign. Visit everyone at the stop off point after the first couple of missions and then you get a key one. Once you have completed this mission you will go back to the stop off point and when you see lots of other online players wandering around then you have the crucible.
Bring up your map but long pressing the touch area on the controller and you will see it.