while I've never lived in an apartment, I did raise a family in a mobile home where space was at a premium to say the least. My reloading operation was done & stored in one of those fake wood grain $49 storage/coat closets from C. T. that have two swinging doors on the front. Total foot print was 15 in. deep X 24 in wide x 6 ft tall. I reinforced the chip board shelving with 2x6 for the press to mount on. The two upper shelves that came with the unit were strong enough to hold the limited amount of bullets and powder that I was using at the time. I installed a lock system on the front doors and it sat against the wall in the corner of the living room for 6 or 8 yrs. I don't remember any visitors even showing an interest in the closet at all.
It was cheap, innocuous,, and really took up no space at all