Search google for "postgres vs mysql" and you will see several writeups. I personally hate mySQL because it has limited SQL support, so it makes my life hell (just like Oracle). PostgreSQL is heaver weight then mySQL but that is not saying a lot. It is a myth that mySQL is faster then PostgreSQL. It is faster for some simple queries, and slower for more complicated queries.
Go with PostgreSQL or FireBird.
That's right, PostgreSQL is more like a heavy-duty database. However, it certainly doesn't move like an elephant. As Dain Sundstrom said in the previous reply, it was an old myth that PostgreSQL was much slower than MySQL. By the time of the benchmarks were done psql was on its 6.5 version, now it's on 7.2 and has quite a lot of improvements (in speed too).
If you like, PostgreSQL is for the open-source what Oracle is for the commercial.
I must mention that last year I conducted a study for my company on open-source database servers and we definitely chose PostgreSQL (running on Linux). And we still use it and never ran into trouble with it. Of course, it's not a professional solution on Windows but MS server is not open-source and is far away from being free. But if your dbserver runs on Windows you can probably afford to use SQLServer or Oracle.
As a personal opinion, PostgreSQL is a consacrated solution, Firebird is quite new; it's based on Borland's Interbase which was made open. And Interbase wasn't really shining (that's way they gave it away for free anyway).
Please keep in mind that these are just personal opinions, I'm not trying to advertise PostgreSQL, on the contrary, on big-money commercial projects I'd rather use Oracle or SQLServer. But in the open...
Have a nice day !
Not to start a war, but Interbase has always been a technically excellent db, Postgres seems to be copying some of its features now. However after 10 years of suppression by Borlands marketing department it wasn't getting many sales. When they tried to kill it, there was a revolt from the developers and dedicated users which resulted in the open-sourcing. Since then Borland has perhaps realized more what they have and have been industriously ignoring the open source efforts and trying to promote their closed version once again.