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.
Although WoW currency can be found through quests, fallen enemies or the dreaded "farming" process, doing it the conventional way is time-consuming. Considering the upcoming release of the Legion expansion pack in August of 2016, stocking up on gold is more important than ever. This way, you can spend less time farming and more time buying everything you need to tackle the next set of challenges.
Take breaks. Unless you're straight up no-lifing it over a weekend or something, this leveling process is going to take ~40 hours. But any time you do need to step away, log out. That tiny little bit of rested exp is insignificant...but you never know when something might come up and you'll have to leave for a longer period of time than you expected. Better to be logged out and safe(especially with War Mode on) than AFK waiting for a d/c. Plus, you'll need to stretch, eat, shower, and maybe sleep. XD
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 late as possible. Early on, you’ll want to follow the missions in Battle for Azeroth right up until you get the option to send a follower on a two-hour long quest. As soon as you get there, stop doing the War Campaign missions. You can come back to them once you have reached something like 119 and a half and finish leveling with those if you want. If you don’t use these missions to cap off your leveling journey, then they’re the first thing you’ll want to do once you reach max level.
I made one for my guildies but its for the Horde leveling process. One tip that goes for both factions is that you dont need to do all 3 zones to hit 120. I did like 1 and than three quarters of another. But once your 120 you need friendly with all 3 of your factions new reps to unlock world quests so make sure you hit at least friendly with all 3 while your leveling.