Final answer:
Software as a Service (SaaS) is the recommended cloud model for upgrading the existing email environment and minimizing server and application maintenance.
Step-by-step explanation:
The cloud model that would best meet the requirements of upgrading the existing email environment and minimizing server and application maintenance is Software as a Service (SaaS). With SaaS, the company would have access to a fully managed email solution provided by a cloud service provider. This means that the email server and application maintenance would be taken care of by the provider, minimizing the need for the company to perform those tasks.