Take photos of all stored items before you store them, and then after you place them in the unit. Keep an inventory of what's in there, with dates purchased, etc. Put the photos on a flash drive, label it, and store it away safely and where you won't forget where it is.
If there is just a cement floor, buy simple rubber mats or place something on the floor to slightly raise up your items. Cement can be damaging sometimes, moisture can seep in, etc. Just get a couple of ugly utilitarian rubber door mats, the kind that allow air to pass through but that would raise something off the floor by an inch or so.
Don't wrap clothing in plastic or store it in dry cleaner's plastic bags or put them in non-breathable storage containers. Amazon.com sells inexpensive, breathable, mold-proof, fabric bags that keep dust and bugs out, but allow for air to get in.
Hide things from plain view. Don't put expensive sporting equipment in plain view if the storage unit isn't enclosed (some just are basically made of metal fences that you can see through easily). Either place them behind a folding screen or put things of value behind a garment rack (you can buy an easy-to-assemble clothes rack to hang things on), and you can hang clothing on it and keep people from seeing what's behind the garment rack. Of course, if this unit is an actual enclosed unit that the passerby can't see into, just ignore this one!
Inform your homeowners or renters insurance company that now some of your belongings will be in a storage unit.
Make sure the lock has at least two keys, and make note of where the keys will be stored. Don't just put them on the key rack with all the other household keys. Store them in a safe, or in another secure place, and make sure that all the adults in the household know where the keys are, and the procedure for returning them after use.