If you're planning on buying a new or used shipping container and don't have the couple thousand dollars on hand to pay for it and have it delivered, you might want to check into financing the container through a loan. While the smartest way is to pay cash up front, it's common for people to get a loan through their bank, pay for it on a credit card, or work out a "rent to own' deal with the seller.
If you have a good relationship with your bank you might be able to get a loan to pay for your storage container. It's not likely that they'll provide a mortgage for the unit, the amount of paperwork, legal work, and underwriting requirements would make the costs associated with it impractical and expensive. The best bet would try to get either an unsecured short term loan, or if you own your home you might be able to tap into the value of your house through a home equity loan.
While it's not the best way to do it, and could prove to be very expensive in the long run, some companies accept credit cards when purchasing a shipping container. It's by far the fastest way to pay for it, but also the most expensive due to the high finance charges that come with buying anything on a credit card. Think of it this way, if you're paying 18% interest on your credit card, and the container costs $2000, you'll be paying an additional $360 for the container IF you pay it off in the first year.
Rent to Own
Depending on who you're buying the container from, they may have rent to own options available. If so, you may end up paying a little more than a cash buyer would, but you have the flexibility to make payments over time and still own the container at the end of the agreed period. As the seller up front if they're able to do this for you and what the terms are.