PostgreSQL is the correct choice as it is a powerful, open-source object-relational database system that supports JSON data types and has robust indexing options for JSON. It can handle complex queries, joins, and it is well-suited for transactional systems. On the other hand, although MySQL supports JSON data types as well, its capabilities for handling JSON and complex transactions are not as advanced as PostgreSQL. Amazon Aurora is compatible with MySQL and PostgreSQL, but the question specifically asks about database engines, not a specific AWS service offering. SQLite is a lightweight database engine that does not offer the same level of support for JSON data types or the same performance with complex joins and transactions compared to PostgreSQL.