Finally: Gearing happens in a pretty linear way for BFA. Once you hit 120, normal dungeons drop 310 and you need 305 item level to start heroics. Heroics drop 325 and I recommend doing Mythic at around 320. Mythic drops 340 and I highly recommend clearing every single mythic dungeon to give you the highest item level going into week 2. On launch, you will have access to 9 Mythic dungeons and there will be 1 dungeon that is gated behind honor bound rep; Siege of Boralus is gated for the Horde and King’s Rest is gated for the Alliance. I am not 100% sure on this, but I do not believe you will be able to obtain enough Honorbound rep to unlock those dungeons with the first week. Either way, its important to get a clear of all 9 dungeons first week to give you the most chances at loot. If PvP is more your thing gear starts at 280 and I am not 100 percent sure how PvP gear works for BFA. I will do more research and fill this in the best I can.
When you have completed your third zone, you should be nearly max level, but you still have work to do! Head back to your faction hub and complete the last foothold quest to unlock your fourth mission table champion. After, you will want to do your newly available invasion missions for your faction. This quest chain is one that will be time gated by reputation levels earned with the 7th Legion for the Alliance and iThe Honorbound for the Horde. Complete as many quests as you can and then finish up your leveling with side quests you may have left in previous zones as necessary.
While the expansion kicks off with heavy references and scenes of this war, leveling through the Horde side of the new content it barely came up again. Except for all the times I had to mine Azerite to make sure my faction was the leader in the Azeroth version of a nuclear arms race. The Alliance side of things had some heavier references to to the war, at least in the portions I played, with one scenario in Stormsong Valley where a fleet of Horde aggressors bombed a town.

Something to keep in mind as well is that this will make enchanting materials more valuable, since it is likely most players will now simply scrap their boe greens instead of getting them disenchanted. Also redundant dungeon/raid gear can be scrapped rather than traded to the (guild) enchanter in the run. Less stuff gets disenchanted, meaning there will be less ecnhanting materials, meaning their value will rise. All the more reason to DE rather than scrap as an ecnhanter.