A Private cloud model would be most appropriate for the company as it offers an environment where services are maintained on a private network and the hardware and software are dedicated solely to the organization. This ensures that concerns such as data control and privacy are addressed since the company's sensitive operations are not vulnerable to the risks associated with shared environments like in public clouds. Unlike public and hybrid models, a private cloud is not shared with other organizations and can offer a higher level of security and control, which caters directly to the scenario involving strict data control policies and privacy issues.