Also get the Heirloom Mount. Being able to have basic riding speed from the beginning will save you a lot of time if you're starting from level 1. Allied races start at 20, so this is a non-issue for them. It's important to note that Pandaren can not use this mount until they finish their starting zone and pick a faction. Being Horde or Alliance is a requirement of the mount.
Drustvar is far and away the hardest Alliance zone, which is exactly why you want to do it first. If you have legendary items, they’ll still be usable, and if you don’t, this zone will still be easier early on than it will be later. Drustvar is also extremely fast and will let you jump out ahead of your competition in other zones, which means fewer players around to take your quest objectives.
Some people have made arguments that quest blues can sometimes be more powerful than heirlooms, especially with sockets. I'm not convinced. The simple fact that you never have to even look at quest rewards will save a non-insignificant amount of time over the course of leveling. Also of consideration is the value of enchanted gear never having to be re-enchanted.
Alpha Beta PTR Classic 1.1.0 1.2.0 1.3.0 1.4.0 1.5.0 1.6.0 1.6.1 1.7.0 1.8.0 1.8.4 1.9.0 1.10.0 1.11.0 1.12.0 Burning Crusade 2.0.1 2.0.3 2.0.4 2.1.0 2.1.2 2.2.0 2.3.0 2.4.0 2.4.3 Wrath of the Lich King 3.0.2 3.0.3 3.0.8 3.1.0 3.2.0 3.2.2 3.3.0 3.3.3 Cataclysm 4.0.1 4.0.3a 4.0.6 4.1.0 4.2.0 4.2.2 4.3.0 4.3.2 Mists of Pandaria 5.0.4 5.0.5 5.1.0 5.2.0 5.3.0 5.4.0 5.4.7 Warlords of Draenor 6.0.2 6.0.3 6.1.0 6.2.0 Legion 7.0.3 7.1.0 7.1.5 7.2.0 7.2.5 7.3.0 7.3.5 Battle for Azeroth 8.0.1
My second most anticipated new feature in the Tides of Vengeance update is the Battle for Darkshore Warfront. It’s the second cyclical battle between the Horde and Alliance, in which each faction takes turns gathering resources, fighting in a pitched raid battle and then controlling the Darkshore zone. In what I hope will be an improvement to the Warfronts feature, the controlling faction will gain access to diverse world quests in the zones they control, rather than the “kill x of y” quests from when it first launched.
Anyway both got to 110 at around 50h played. I messed up with my Pal by going to Legion once I hit 100 instead of finishing treasures and bonuses in WoD. All in all, if I picked the best zones and was only trying to level as fast as I could, I would probably could have done it in roughly 40h. Note that it would have a been A LOT faster with a Monk as both Ret and Rogues don't really have a decent AoE until 40+ (45 for Ret and 63 for Rogue I believe). The daily also helps a lot. I know that leveling my Monk before the pre-patch was insanely fast. Might be slower with the changes to FoF, however.
Do quests and complete the story of your first chosen area before returning to your capital to scrap all of the equipment items you acquired. You should be around Level 113 by the time you complete your first area. Before selecting your second zone, head to your faction hub ship to acquire your introductory quests to the mission table and your champions. Complete this introduction and then pick up the quest to establish your first foothold in enemy territory. 

Still, it’s terrible to see the new expansion fail so spectacularly at iterating on Legion’s success. It’s hard to believe the two expansions came from the same company. Legion made you feel powerful and unique. Battle for Azeroth grinds at you by taking away as much as it gives. Sure, you can have a shiny toy. Sometimes. If you don’t get too carried away.
I do not recommend going for TBC, although I remember Hellfire peninsula to be decent, everything else is rather slow. Instead go for WotLK, Borean Thundra gets you levelled very fast, and then you can head straight for Icecrown at 67, which is also insanely fast, although admittedly has a few elite quests. You can go to Sholazar Basin alternatively. 2 zones should get you 60-80 no problem.