The most frequent lock used is the basic hardened steel padlock found at the big box and hardware stores. These locks are the least secure and easily broken with a bolt cutter. To keep costs down on these mass produced locks the manufacturer only produces a small number of key combinations. What this means is that the person buying the same lock right after you could have the exact same key. These locks are also easy to pick even for amateurs. This means that theft can go undetected until you re-enter your storage unit weeks or months later. This type of lock belongs on the yard shed, not on your self-storage unit.
A significant upgrade is the disc lock. The shackle is hidden inside the round shape, making the lock virtually impossible to use a bolt cutter on. It is possible to cut these locks with a grinder, but the time and noise involved to break the lock are an ample deterrent to this method. This lock is also more difficult to pick. Fortunately, a number of disc locks feature dimple type keyways with dimples and grooves cut into the side of the key, meaning that there will be over 3000+ key combinations. They can be bumped but the level of difficulty means you are dealing with an expert thief and not the typical break and enter amateur.
Ultimately, the best lock to protect your belongings is the silver disc lock.