I think what makes this request much easier is the fact that the poster only wants to make sure that they don't delete each others' files. The first Wiki article on Groups explains how to set this up. By making the directory group writable, they can upload. Whatever they upload is not group writable, so the other user(s) won't be able to delete their file.
Unless the original poster wants some sort of superuser control of what's uploaded, it's straightforward. Although being the owner of the plan, the original poster will have access to the other users' passwords, so if necessary, the owner can log in under these other accounts and make any changes.