Unless low quality items have some known quest use or are coveted by other players, you should try to sell it as soon as possible to create bag space. Always (or almost always, see above exceptions) keep things like cloth, leather, herbs, or large stacks of white/gray items over other loot when you have to decide what to keep when your bags get full. It might be worth your while to invest in larger bags (10-20 slot), especially if you know a tailor.
Just before Battle for Azeroth goes live, you will want to log all of your characters out in the zone of Silithus so that you can acquire the quest to talk to Magni and obtain your Heart of Azeroth (refer to our Heart of Azeroth guide for more information about this item). This is the new artifact-type of piece of equipment that you will use for all of the Battle for Azeroth expansion. Once you acquire your permanent neck slot piece of equipment, get back to Stormwind or Orgrimmar to begin your scenario that leads into the introductory areas of Kul Tiras and Zandalar.