Azure Kubernetes Service (AKS) is the most suitable option for hosting a complex, multi-tier application composed of microservices. AKS simplifies the deployment, management, and operations of Kubernetes and provides features such as auto-scaling, self-healing, and load balancing, enabling the team to manage each microservice independently based on its specific requirements. Choosing individual virtual machines would not provide the same level of operational efficiency or the orchestration benefits needed for microservices, and while Web Apps and Azure Functions are suitable for specific scenarios, they do not offer the same level of control and flexibility required for complex microservice architectures.