Educate yourself about mobile storage
Then you can just call the company again for pick up after you have filled up the containers. Just give them your most convenient time to receive them and they will move them to the destination you specified. Or you can have them kept temporarily at one of their storage facilities. In case you are too busy yet and decided to have them at their facilities, you can have access to the container anytime you want. If you chose a reliable company there is no need for you to worry about the safety of your things.