It won’t take long before your in the latest 8.3 raid Ny’alotha, which requires 410 to queue in LFR. The Eternal Palace LFR raid from 8.2 requires 380 I believe. Get the “send the fleet” quest from the ship on Zuldazar south docks, which sends you to the Nazjatar zone story quests. They give you a 370 weapon along the way. When you get the Magni quest to go to chamber of heart. Run those quests to unlock essences.
World quest gear scales up to 420 now (445 emmisaries) and the gear item level rewards increase on the map instantly when your item level goes up. Last time I checked 400 trinkets and some weapons were cheap on the AH.