My MESON chess problem database is powered by MySQL, a database that is made available by many web hosting companies. It has become the standard for web-based databases. There are community editions that are free and downloadable to run on Windows or Linux. So, I have it installed on my Linux PC here at home and can develop there and then implement at the web host. There are freely available APIs for C, Perl, Java, Python, PHP and, no doubt, other languages. See the MySQL website for full details.
Developed and maintained by Brian Stephenson.