Here are some simplish easy to live by ideas I had to deal with when I faced the same problem as you. (I came to Eorzea expecting ingredeint drop rate to be comprable to Vana'diel... I was shocked!)

If the item you have is ...
1) Sold from NPCs for cheap, sell yours. Buy it from NPC when needed.
2) Sold cheap and plentiful in the wards, NPC yours. Buy it from Wards when needed.
3) Easily farmable (you've seen it drop many times), NPC yours. Go farm again (or buy from wards) when needed.
4) Only small in quantity (1,2,3 rather than 99). NPC it. 20 assorted items in quantity of 1 or 2 just eats up space and does not really help you when it is crafting time.

Unless you've been farming specifically, chances are anything you've 'picked up along the way' is not that valuable. Anything that can be used for low level synths are not that valuable.

Once I adhered to this, I sold almost all the crafting materials in my inventories.

If you are pressed for Gil, you could check up the price of each item... for me, a few went for 4-10k each so at the end of the day I sold a 80% of my stock to NPC and the rest for about 50k total (which was a lot for me, as I have a bad habit of turning all my equipment into Materia).