Assuming you have the Heavensward hunts unlocked, if you can get in a handful of those you can buy the ilvl 200 gear for centurio seals in the Forgotten Knight. That will also give you scripture and lore (as should POTD). The lore tomestones will get you the 230 gear.

If you can tolerate endless POTD runs your most efficient approach is probably to run that for lore to get the 230 gear, the 255 weapon, and fill in with scripture gear (260) as available.
For the 255 POTD weapon I recommend saving up to +90 all at once. Levels 51-100 are more interesting that 1-50 imo and they go faster with a better stats.
Once you have some lore gear you can run Void Ark and then Weeping City to get tokens to upgrade it to 240.
Your next step is getting to ilvl 230+ to get into Alexander Creator for 250 gear. Alex Creator and scripture are both currently limited per week, so this is where things slow down. If you have enough gil there is also crafter 250 gear.
The only way to currently get gear over 260 is Alexander Creator Savage which requires ilvl 245 to even set foot in. Without the crafted gear you could still theoretically reach that in a week - 255 POTD weapon, scripture accessory, at least 2 pieces of Alex Creator gear, and everything else upgraded lore.