Amazon DynamoDB is the correct choice as it provides a scalable, NoSQL database service designed to handle high-traffic applications with unpredictable workloads and highly variable database access patterns. It offers a serverless option, which can automatically adjust capacity to maintain performance without the need for provisioning or management, thus optimizing costs. Amazon RDS is more suitable for applications that require relational database capabilities like complex joins and transactions, which were specifically not needed in this scenario.