The absolute fastest way would be to buy i255(?) gear off the market board, but that could be costly.

As mentioned, pvp gear is i235, lore gear is i230, scripture gear is i260, centurio seal gear is i200.
There's also alexander gear I believe, but I don't know the stats of those offhand.


All valid options to help increase your item level.
All with varying speed and grind requirements.


If you go with a grind...
PotD may be your best bet.
You can get poetics, lore and scripture from it as a 60, as well as build up aetherpool level to get an i235 weapon.

You can use the lore and scripture to buy i230 and i260 pieces to build up your item level as you can.

The quest to unlock it starts in the gridania adventurer's guild if you haven't unlocked it yet.
The house that death built, is the quest name iirc.