AWS Lambda is the best fit for this scenario because it's designed to automatically run code in response to events without provisioning or managing servers, which is ideal for workloads that are unpredictable and fluctuating. This service ensures that the application can start quickly and run whenever it is triggered by an event, which is optimal for processing transactions in the scenario described. Other services like ECS and Fargate also offer serverless options but are generally more suitable for long-running tasks and instances where container management is preferred.