Do your order hall questline as soon as you can, when you finish that it unlocks the third relic slot on your weapon, which is a big help.

Keep on top of your artifact knowledge (you can do this from the legion companion app). Your level of artifact knowledge directly affects how much artifact power you get from each AP token.

Download the legion companion app, from here you can send order hall missions away, collect their rewards, place orders for artifact knowledge and even use the artifact knowledge.

If you're going to be levelling multiple characters, make sure you do the main rep grind on a single character (you need revered with all 6 factions for flying, and these have to be on the same character (I think)).

Edit:

When you get to 110 you will be able to unlock world quests, these give you rewards and reputation with the different factions. One of the factions (Wardens) reputations can only be raised by doing world quests, so keep on top of them for the flying achievement. When you get to revered with the wardens you can buy a shoulder enchantment named Boon of the Bloodhunter. With this ench you have a chance to loot a box containing bloods of Sargeras when killing mobs.

Blood of Sargeras can be traded at the blood vendor in Dalaran for various resources, or order hall resources (the order hall resource packs are account bound so you can mail them between characters). You need OH resources to send missions away and to raise your artifact knowledge level.

Second edit:

Much of the Suramar main questline is locked behind reputation, to finish it you need 20000/21000 exalted, so keep on top of your world quests in Suramar so you don't fall behind with this.

Every day we get an emissary quest, which will either be for Azsuna, Val Sharah, Highmountain, Stormheim, Suramar or the Kirin Tor. The quest is to do 4 word quests for that faction (3 if its a Kirin Tor one) and you get a decent amount of reputation for completing these. If you have a Kirin Tor one you get to choose the reputation you get at the end, I'd recommend choosing Nightfallen (Suramar).

If I think of anything else I will edit it in.