My toon was a monk, a class that gets extra experience for an hour at a time. I picked at it more than I have in the past, so I benefitted more from the 150 percent "rested" experience bonus. If I wanted to run a dungeon for quests, I fired up a high-level character on a second account and dragged my little toon through them. And having leveled dozens of characters to 100 and 110, I knew every zone and every objective.
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.
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First up we have patch 7.3.5, which was implemented several months ago as a major shakeup to how leveling was approached. Instead of going from low to high level zones like the way the game had always operated, Blizzard opened up the map with more of a Guild Wars 2 type system -- you now have more of a choice of where to go with a scaling mechanic. But when combined with 8.0's massive stat overhaul, things got murky.
Fourth: This is very important; do not vendor the gear you obtain while leveling. There is a new mechanic introduced in BFA called the Scrapper which allows you scrap your gear for trade goods which will be very important for rep and AP grinding (will talk about it more later). Usually after I clear a zone, I will head to the scrap bot and scrap all my greens/blues to clear my bag for the next zone.

Potions serve more utilitarian purposes, and it's up to you to decide whether to make use of them. The most common is the Swiftness Potion, which can provide you a handy boost in speed while going after annoying quest objectives indoors. These are generally MASSIVELY overpriced, because people know how useful they are. I opted not to spend the gold since Warriors are already fairly mobile, but slower classes may benefit greatly from these.
You earn a large rested experience bonus when you log out in this rest areas. This gives you a massive 200-percent bonus to experience gain from most actions (though experience from quests isn’t included). The amount of rested experience you earn increases the longer you’re logged off, and your experience bar will be blue (instead of purple) while you have the bonus.
I'm with that guy, I'll probably pick whichever zone I want and not follow a set path for the questing experience itself (like the part about not picking up the treasures, if I see a shiny I'm going for it lol), but I'll come back to this post for the gearing/rep-gain stuff. Thanks for taking the time to type it out. Also the bit about scrapping gear instead of selling it was something I hadn't thought of so thanks.
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.

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.