Azure Blob Storage is the correct choice for storing a very large collection of small user avatar images because it is cost effective object storage that scales massively and offers tiering to optimize costs based on access patterns.

Azure Blob Storage is designed for unstructured object data and charges primarily for stored bytes and operations which makes it cheaper than database or file services when storing many images. You can use hot, cool, and archive tiers and lifecycle management to lower costs for objects with different access patterns and you can combine it with a CDN for efficient global reads.

Azure Files provides managed SMB and NFS file shares and is intended for scenarios that need file system semantics and lift and shift migrations. It is not the most cost effective option for simple avatar image storage because it typically costs more and adds features that are not required for object storage.

Azure Cosmos DB is a globally distributed NoSQL database that charges for storage and request units which makes it significantly more expensive for storing large numbers of binary blobs. It is optimized for low latency queries and transactional data rather than bulk object storage.

Azure Data Lake Storage Gen2 builds on blob storage and adds a hierarchical namespace for analytics workloads. It is aimed at big data and filesystem semantics and is not the most cost effective choice for many small avatar images unless you specifically need analytics or hierarchical file operations.

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