Option B, deploying an Amazon CloudFront web distribution in front of the S3 bucket, is the most cost-effective solution. Amazon CloudFront is a content delivery network (CDN) service that securely delivers data, videos, applications, and APIs to customers globally with low latency and high transfer speeds. By caching content in edge locations around the world, CloudFront reduces the load on the origin S3 bucket, thereby improving performance and reducing costs. The other options involve caching or accelerating web servers, which are less suitable for large-scale distribution of static media files.