If you need the abridged version, because you’d rather spend an hour in a game than hearing someone talk about a game, you can also check out the excellent “New & Returning Player Guides” series from YouTuber (and World of Warcraft expert) Bellular. And you probably even skip the bits about ”how to purchase” or “how to install” the game, saving you even more time for new World of Warcraft adventures:
For Alliance it's Lok'Modan, Redridge, Darkshore, Felwood, Stranglethorn (both parts), Plaguelands. Somewhere between 3 - 3.5 of these get you to 60 in like a 16 hours /played, if you queue for dungeons at the same time. I recommend dropping everything at 45 and going to Darkshore-Felwood if you didn't do them yet - they are literally the fastest levelling zones in the game right now, maybe only trumped by Silverpine.
Heirlooms are special pieces of armor that level up with your character, so they have stats that are always respectable for your character’s level (up to level 110). Heirlooms that fit the head, shoulder, chest, legs, and back armor slot offer an experience bonus. The total bonus is 45 percent if you have them all. It’s also possible to acquire a ring that adds another 5 percent, but you must win a fishing contest acquire it, and that can take some time.
Once again, as soon as you hit 70 - I recommend to go and learn faster flying. This speeds up your questing A LOT, and is worth the time and gold. It will cost 4500 if you go to the capitol, or 5000 if you prefer Shattrath/Dalaran, because you will not have reputation with them at that point. This price will sadly be above what a totally new character can afford, if you don't have any Main. But you should go and buy flying as soon as you have enough money.
Havoc in Battle for Azeroth has gone through somewhat of a maturing process, trying to focus more on the talent tree and allowing for more diverse options in gameplay approaches, alongside tightening up some of the more loose aspects of the original implementation. It still remains a predominantly builder spender style rotation and is largely Global Cooldown locked. The core hook is making the most of your Fury pool and reacting to unpredictable gains, ensuring you use high burst cooldowns and windows to push yourself even further. On top of that, it comes with a variety of mobility and defense tools, creating a versatile toolkit with some unique abilities that can be used in a variety of ways.
Tiragarde Sound and Stormsong Valley are both fairly similar zones, but Stormsong is a little longer, meaning that you might not even have to finish it to hit 120. Tiragarde also comes with a bit of a warning. There are plenty of side quests to do in the zone after you finish the story quests. Don’t do them. It’s not worth the time or the experience you’ll get. 
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