depends on what you actully need to build , but as i understood , you want to build a database using sql , with no need to be published on the internet or to be on a server , u can build a "local" database using MySQL 5.5 command line client
you can download it from here : http://www.mysql.com/downloads/mysql/
and when u do so , open the command line client and start using SQL to build your database.
additional details answer :
OK , when your are finished creating the database and inserting the data you want to insert in its tables , u can export the database using your computer (check MySQL reference on their website for how to export databases using MySQL) and import it using any computer / server that has a database management system installed on .
about database being only searchable , not editable by users , this is possible by any DBMS , mysql , sqlite , MSSQL , even access , its about permissions , the database administrator is the one who assigns permissions and creates views of the database tables as needed.
don't forget to chose the right engine for your database , if you have many foreign keys and need to use transactions , you would need to use innodb , which is the default engine that MySQL 5.5 has.