Rubies, diamonds, sapphires, Topaz, amethyst, obsidian, and emerald- 7 jewels
I have chips up to level 5 stored on extra items
Potentially 5x7= 35 inventory slots holding 1-5 chips - call that 30 slots

Speakers take up a slew of slots in inventory- Being guild host, I occasionally need them in large amounts
blue and purple medals work best in batches- so I save them up as well
Labyrinth tokens- need to save 100 to buy lightbringer spirit plans
Need six open slots for swapping out gear between heroes for various fights (cerberus, heroics, ragnarok, labyrinth, etc.)
Holding extra Hero Cards for a reset (perhaps a batch of ten...)
Oh, and for holding occasional plans and items for crafting

Yes, my inventory gets crowded...