The database is not the main task to be solved - it is a database with a useable user interface.
You can run MySQL, MariaDB for free or use cloud based stuff like MongoDB or FireBase.
If you do have structured data - and within a database that should be the case - you can export the data into any other format like JSON, XML, CSV… and import it back into TBX.
But the databases themself offer no user friendly interface. There are tons of apps like MySQL Workbench, dbForge Studio… but none is fun to use.
By the way - devonthink uses a database with an acceptable interface.
P.S.: my WordPress PlugIn for TBX is more or less an interface for a database to be used from TBX. But it is a one way communication interface at the moment and WP comes with some overhead on top of the pure little database behind it