I recommend you try SQL Server Express, it is the easiest server you work with if you work with C #. If you want to learn SQL using Java, almost any database would be good.
A database server is software, like any other, you will have to communicate with it through your own program, creating a connection, throwing SQL commands and interpreting its results. If you only wanted to learn SQL, you could also install the client for the selected database server and study it, after which you could try to connect your program to this database. In this case, SQLite will work very well for you.
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