To host a MariaDB database in the AWS Cloud with the least amount of operational overhead, Amazon RDS is the most suitable service. Amazon RDS is a managed relational database service that can handle administrative tasks such as hardware provisioning, database setup, patching, and backups, which significantly reduces the operational burden for the company. Services like Amazon Neptune and Amazon DynamoDB cater to different types of databases (graph and NoSQL, respectively), and Amazon S3 is not designed for hosting relational databases.