The type of lock which is safest for a storage unit can change very rapidly. It can also be influenced by various factors including exposure to the elements, the last thing you want is rain causing corrosion or jamming the mechanism. Or, sun damage leading to seizing of the lock.
When your secure storage unit is within a dedicated self storage unit facility, that is undercover, the choices become simpler in terms of what type of lock to use.
One point that is worth considering, and often remarked on by security experts, is about having locks which blend in with their surroundings.
Sometimes, it can be more secure to have a less secure lock that blends in with those on other secure storage units, so that no-one is drawn to your unit due to the type of lock it has. High security locks being used when other people have simpler locks, can trigger people to think about what is being secured, and whether they should attempt to force access themselves.
Combination padlocks are about the last thing that should be used on secure storage units. While they do save problems if keys are lost, they do require combinations being kept secure. Most people will need to write down a combination, if it is a random one, and writing down combinations brings further security issues.
Anything with a long shackle is unwise, as the shackle tends to be a weak point which can be easily cut or forced. Disc locks, or round shackle padlocks are good for security. They have very little of the shackle exposed and as a result are very difficult to cut open with bolt cutters or saws. Plus, most have to be locked with a key, rather than just pressed closed, making them good for use in secure storage units.