There are three databases you should probably look at if you're looking at Open Source or Free Software databases.
Interbase, now firebird. Mature, runs well on both windows and linux. It is built as a medium load handling transactionally capable database, and is most commonly used for intranets and such. License if Mozilla (i.e. almost BSD)
MySQL is a great mostly read, some write data store for content management and datamining. It lacks some of the finer points of other reliational databases, but makes up for it in very simple administration and good speed. With the 4.x release transactions and foreign keys show up, and by 5 or 6 subselects and other useful sql features like stored procedures should be available. License if GPL
Postgresql is a descendant of a Berkely project (three things came out of Berkely, Unix, Ingre/Postgres, and acid, and those things probably aren't wholly coincidental ;) It is built for very heavy parallel load, but requires more system administration experience than either mysql or firebird. It also lacks the fine grained security of mySQL and firebird which are needed in an environment where many users who don't know each other are developing. This makes it a good choice as a dedicate dbms for an intranet or single large project, but a poor choice where hundreds of strangers share the database. Most of these issues are soon to be addressed by the 7.3 release. License is BSD style
