My old barn had an empty box stall with saddle racks in it as the tack rooms. Bridles were hung on individual horse's stalls. You could keep your own stuff there (saddle, pads, grooming supplies etc) if you rode more than once a week. People mostly used smallish Rubbermaid boxes for everything but saddles and pads. I had things stolen multiple times...Nothing expensive, but it was rather annoying. List includes bit wipes, lead rope, braiding bands, grooming block (used it excessively without asking), and for a short time my scissors were "missing..." and it happened to be while the barn owner (!!!) was cutting some horses' tails and feathers. The scissors mysteriously reappeared the next day...Yes, they were labeled, stupidly with a piece of tape with my name on it. Tape was gone after the incident.
New barn has a tackroom with all the saddles and horse's bridles. It is locked at the end of every day. I have my Rubbermaid bin there but it is in the attic, which most people don't even know exists. I feel my stuff is secure there especially since right now it is used mostly for storage of blankets. If/when I get a tack trunk I will be allowed to keep it on the first floor. I'm not exactly sure where it will be, but it will have a lock so it doesn't matter.
"The wise man thinks he knows nothing.
The fool thinks he knows everything."