Skip the faction gear to be honest - if it was tokens only that would be one thing, but the amount of gold you also have to spend is better saved unless you're rich as fuck.
If you need a token dump, you can buy the token cost only gypsum orbs daily. You'll also eventually need chromatic seals - artifacts will take 1 seal to customize the 3rd perk/level them up in the gypsum furnace and upgradable named drops from dungeons will cost 3 seals to customize the 3rd perk. Seals cost like 20k tokens 5k gold each and it is a once per day thing. Armor and Weapon Matrix usually go for around 10k or so on auction house. So for example if you wanted to upgrade some named dungeon drop in the gypsum furnace, that means over 25k gold per item when you count the seal and matrix costs. You don't HAVE to do that, but then you're dependent on RNG for good drops. All the gold you got from leveling up gets drained fast if you aren't careful.
Chest runs and dungeon runs will net you some decent gear that is better than 675. I'd do chest runs until you have enough high GS pieces (you could literally fully gear in random shit after a world tour), then you can try to target stuff in dungeons for specific builds. Also remember that chests have loot bias - so if you're wearing light armor and using a fire staff, you're gonna get mostly light armor and firestaffs. Wear the type of gear you want to get to get better types of that gear