Make sure you have the two Flight-Path toys purchased, as this can save you time. It won't have EVERY flight path, but will have major locations for faster travel if you need to switch zones entirely(which you will). If you buy the toys on one faction, it unlocks for the other faction as well. So don't spend double the gold! These toys can be found at the heirloom vendor(Undercity for Horde, Ironforge for Alliance)
The Horde 12-25 (Barrens + Stonetalon Mountains) guide has been rewritten and revamped. In addition, there has been numerous tweaks to the speedrun route to make things faster and easier to follow. Also, in case you haven't noticed I am now adding about 40% more info per step and redoing all the images. Unlike with my previous vanilla guides, I am now giving a brief explanation of where to go and what to do with each step along with any other helpful tips.
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Special note: At 110 it's almost certainly worthwhile to go and immediately get your Heart of Azeroth and first piece of Azerite gear from the BfA opening quest. It doesn't take long and provides pretty high power levels. I'd then return to Legion quests until 111 or even 112, since the power of these items will increase your kill speed significantly over the scaled enemies of BfA content.
As you're leveling, I generally recommend you just follow the natural flow of the progression through each zone. They're laid out fairly reasonably. But don't be afraid to hop around, especially if you're near a quest objective. You shouldn't actually need ALL of the zones listed to reach 62. Pick the ones you like best. It's much more important to simply be as focused as possible and flow from one quest to the next.
Just before Battle for Azeroth goes live, you will want to log all of your characters out in the zone of Silithus so that you can acquire the quest to talk to Magni and obtain your Heart of Azeroth (refer to our Heart of Azeroth guide for more information about this item). This is the new artifact-type of piece of equipment that you will use for all of the Battle for Azeroth expansion. Once you acquire your permanent neck slot piece of equipment, get back to Stormwind or Orgrimmar to begin your scenario that leads into the introductory areas of Kul Tiras and Zandalar.
Like most of those experienced players, I had all the benefits, including a full set of heirloom armor, which helps to boost the experience my character would get (though that bump was reduced at the same time the other changes were made.) I had a guild, the ability to fly in every zone, and pets and toys that made a pile of things more convenient. My new character started at level 20, as all allied races do.
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