Firebird seems to a pretty complete product but the documentation is awful, so I haven't used it much.
I've used MySQL and Postgres a good deal and strongly prefer Postgres. It has tons of advanced features and follows the standard closely. And given the right circumstances MySQL can be amazingly fast. But MySQL's strongest selling point is probably its popularity.
But the right database for you largely depends on you. If you are an enterprise user coming from Oracle or DB2 then hands Postgres. If you are a web developer that just wants some place to stuff your data then I'd recommend MySQL.
MySQL is more simple... than PostgreSQL; it's fast, easy and have a good documentation.
MySQL have a good tool (phpmyadmin, areosql and more...) for management (via web).
MySQL have tow license, free and commercial.
MySQL is more slow than PostreSQL with an elevate number of requests.