Congratulations on reaching Level 120! There are a myriad of new things to do. The first thing you should do is head to your faction hub ship where you have been doing your mission table quests and footholds to pick up and complete the quests necessary to unlock World Quests. World Quests will provide you an opportunity to grind reputation levels, acquire gear, and gather Azerite. There are tons of new things to do that we will cover in our Level 120 Battle Guide found here: Level 120 Battle Guide
Fifth: As for Azerite Armor, I recommend getting the Chest first from Magini and if you do Vol'dun first, the first piece you can get will be a Head and the final piece from the zone with be Shoulders. That will give you all 3 pieces of Azerite Armor when you leave the first zone which will help out. If you are leveling a different spec from what you plan on playing, (i.e leveling as a dps when you plan to heal/tank) you will receive at least 2 pieces from every zone then 1 piece from starting the War Campaign that you can choose your Main Spec trait for. Pick the traits that will help you level the fastest.
The leveling guides on my site are essentially speed leveling guides. My leveling guides are the same guides I use myself to speedrun to 60 on new servers to get 60 server first. I list many occasions where I tell the player to "die on purpose" to go faster. I tell the player to skip certain quests, because some quests are just not worth the time/XP. I list tricks and shortcuts to go faster so you can reach level 60 much quicker. I am still constantly going through them over and over again perfecting the guides to make them faster and easier to follow. For the most part, the guide can be followed without the need from other player's help, as the whole guide was made from a solo run anyways. Although I do list quests that can optionally be done if you have a group.
In particular, between 2014 and 2016, it was possible for dedicated players to generate quantities of gold that were previously impossible to obtain, and have not been possible to obtain since. The Warlords of Draenor expansion was the first time the game included nonplayer character followers that players could send on missions to collect resources, items and other useful stuff, including gold.
Literally just do quests as efficiently as you can. The difference between picking a perfect route and just doing whatever is like an hour, tops. I've already leveled 7 characters in bets because I won't be playing at launch (baby due in aug) and I've been under 12 hours on all but the first. I actually broke 10 on DH, but that's bcuz war mode and DH leech is OP, not because of a special route.
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Edit 20 It’s been a week since this post and a lot of people are still reaching out to me with questions which is fine. I have had a few different people reach out to me to help make YouTube videos based off this guide and more info in BFA which I’m more than willing to do. Whoever gets the videos up first I will link them here for you guys to enjoy.