Unlike Legion, BFA reputations plays a significant role in gearing your character and progressing on storyline;
The most important one is Champions of Azeroth, because a progress with it impoves your neck's ilvl. It is the only way to upgrade azerite neck's ilvl aside from AP world quests.
The second important one is The Honorbound/7th Legion, which unlocks War Campaign story chapters and 2 Mythic dungeons: The Siege of Boralus / King's Rest.
By the time raid is opened you'll have 4 of 6 factions at Exalted. The last one is Tortollans (Revered). I don't think it's possible now to hit Exalted with Champions after contracts nerf. But you still want revered with them asap
You'll spending most of your time raising your reputations. It is the best way to rise your ilvl before M+ and Mythic Uldir are opened.
Important note to farming reputation is the Contract - a scroll recipe at Inscription level 75 that costs 20-30 herb.
During the buff you'll recieve +10 rep of selected faction when completing any world quest.
The priority is to have Champions of Azeroth contract buff, but you can only use it after reaching Friendly. Use any other contract in the meantime until you hit friendly.
Goals for the first 3 resets before M+ and Mythic Uldir are opened:
Main character and alts are level 120;
Main character's gear is at least 350 ilvl by the start of the 4th reset;