I tried storing all the clothes I'd been carrying around in my inventory in the bin in your captain's quarters, but they keep disappearing so I was wondering if anyone knew a better spot to store stuff
All of the containers in the Fallbrook domicile (reguires key) are safe. I left an adreno in each container then forgot about them. There are still there so.
I've used the Captain's quarters and the lockers downstairs (near ADA and the exit from the ship), so I'd say you seem to be encountering a bug if it's making all your attire disappear.