1. Wrap What You Can : Wrap what you can in industrial plastic wrap. That way things are sealed up tight and it won't collect dust.
2. Label, Label, Label: Even though you know exactly what you're putting in your storage unit at the time you rent it, that doesn't mean in 6 months when you need back in it that you won't be digging for ages. Prevent opening random boxes until you find what you're looking for, label everything.
3. Plan For Temperature Changes: In Arizona there are a few things that don't like the heat and should either be double wrapped or well insulated or not stored at all. Electronics, vinyl records, things of that nature all come out a little less awesome when not stored properly.
4. Bust Out Your Stacking Skills: The smallest storage unit can hold a great deal. Make sure you use the space wisely which means packing things all the way to the ceiling. Bringing in plywood to lay across several boxes can help stabilize layers as your stacking it up, up and up! It will take the pressure off the tops of your boxes and help keep things safe.