This should take the most thought. There are some great website about choosing your database.
- SQL(Relational) Open Source Options
- Postgres
- MySQL
- MariaDB
- SQL(Relational) Commercial Options
- Oracle
- Microsoft SQL Server
- IBM DB2
- NoSQL Options
- Cassandra (wide column)
- MongoDB (document db)
- Redis (key/value)
If you are unsure, Postgres is always a great safe choice. There are some powerful NoSQL options, but like anything, they are a solution. Meaning they must fit the problem. Start with the data and the needs of the data, then that will drive the DB options.