Diane,

If you are talking about a local move between two storage locations I would suggest you to do it yourself, especially since most storage locations provide you with a free van + driver. If movers need to be used then just have them do the move in one day (after all its between one storage and another), although they would probably charge you minimum fee which can be over $300 in some cases.

If your move is long distance then you should be aware of the minimum weight requirement that many companies have, and a delivery window that you must allow them (usually 1-4 weeks depending on the distance). Having that in mind it would usually help to know that most long distance movers provide you with one month free transitional storage, although if you ask my honest opinion I would say that your items are better off locked in your private storage room then in one of those transitional storages (its like many restaurants - you will enjoy your food as long as you haven't seen how it was prepared...).