It seems like most people use MySQL together with PHP. I've used H2 and Postgres with Java, but I can't really say why, I didn't evaluate any before I started.
Most people who use a programming language use a similar DB. While this is not always the case it does make it easier to find example and get Help on forums etc if you are using a set up that other people are familiar with.
I guess it all depends on the size of your DB and number of transactions also.
Postgres and MySQL are popular for Linux (and windows), MS SQL express edition is also free for under 2Gb of data and comes a lot of goodies.
See http://stackoverflow.com/questions/1373566/what-is-the-best-dbms-for-the-job