In this scenario, the best cloud service model would be IaaS. This stands for Infrastructure as a service (IaaS) and basically provides all the physical infrastructure that a company needs virtually. The company itself purchases a piece of software that allows them to remotely use all of the infrastructure provided by the service. Meaning they have access to computing power, data centers space, servers, networking, etc. without actually purchasing any of the physical hardware. This would solve all of "your" business needs as asked by the company.
