Keep an eye on what you really need and their billing schedule. Also go through all your stuff and throw half of it out.
This. If you absolutely need a storage unit, you want to be filling that space so it's filled to the brim. No walk-in room, no space at the top, nothing. Disassemble any furniture, if you can. An extra $30/month on space you don't need adds up. Also, make sure that they have at least some kind of limited area access, let alone cameras and 24/7 security. It depends on the area, but in general, these aren't premium features, any serious storage area will have at least the first two.
Also, be careful about how they handle move out. Some places will try and get you to sign up for their "expedited move out service" or some such when you move in, and charge you $hundreds for their "help" when you move out.
Get a real lock. Bare minimum, get something with a rotary shackle (locks via a circular movement of the actual shackle) and a shroud. A rotary shackle means that someone with a hammer won't be able to just knock the lock off with a downward strike, and a shroud covers most of the shackle, so it will be much, much harder to cut off with bolt cutters.
I used a
Master Rotary Shackle the last time I stored stuff.
Added at: 18:32
EDIT: Also, make sure that your insurance will cover any possible theft. If it won't, you can buy insurance from them, but investigate the rating of their underwriter before you sign anything.
Storing your stuff is just like insurance, actually. You want to be paying enough to get the coverage you need, but you need to watch out and make sure you're not paying for things you don't need or paying extra for standard or substandard service.