To design Google Play Store, I'd first identify key user personas (developers, end-users) and derive functional requirements, prioritizing them using MoSCoW. For data storage, I'd use a relational database (RDBMS) for structured data like user profiles and app metadata, ensuring ACID compliance. App binaries, however, would be stored in a highly scalable, distributed object storage system like Amazon S3 or Google Cloud Storage, with the RDBMS storing URLs to these binaries.
For scalability and availability, I'd implement sharding and partitioning for the RDBMS to handle large datasets and high traffic. Replication would be crucial for fault tolerance and read performance. Caching would be employed at multiple layers: CDN for static assets, in-memory caches for frequently accessed app data, and database query caching. Load balancers would distribute traffic across multiple servers at various tiers (web, application, database).
Considering the CAP theorem, for a system like Play Store, availability and partition tolerance are paramount, often favoring an AP system for certain components, while strong consistency might be prioritized for critical transactional data.