When my Mother moved in to a nursing home I put her belongings in storage. They have been in a U-Haul climate controlled, multi-story, storage facility for fours years now, in Central Florida, with no issues....yet! Based on that type of facility my suggestions are:
1. Choose your storage facility very carefully. What type of security systems, fire control, video recording, and access type and hours do they have? Check with the local Police Department for the facilities "record"...you don't want a place with a lot of break ins on their record.
2. Buy insurance! The facilities insurance won't cover your belongs or will provide only minimal coverage. You need to document what you have, adding digital photos is good, and insure it. Check very closely for exceptions, most basic insurance will not cover high dollar valuables such as antiques, jewelry, expensive electronics, weapons, and other high value items. You may be able to cover them with separate policy "rider".
3. Climate Controlled is a "must have" to help prevent mold and mildew in humid areas. And a good idea anywhere else. Photos, documents and other papers do not fair well in non-climate controlled storage. Clothing runs a close second...
4. Stay off the ground floor. In the event of any water damage the first floor is the worst floor.
5. Stay off the floor in your unit. Put everything on shelving units that keep your "stuff" a couple of inches off the concrete floor. This will help protect against water damage to a degree.
6. Air flow. Allow for air flow around your "stuff". That will help minimize mold and mildew caused by over packing the unit.
7. Make sure the storage owner is doing pest control. Rest assured one of your neighbors will try to store food stuffs...
8. Locks. Any lock can be defeated or the thief just cuts off the hasp itself. So don't go over board. Purchase a good high security padlock and make extra keys.
9. Periodically check on your belongings. Heading off any problems early is the best way to prevent serious damage.
Hope this helps...