Which database engine you can use also depends on whether you are using MS junk or some other computer as well as which operating system you have on that computer. Example: If you are using an older Mac, you cannot use MySql, but you can use FoxPro (good luck in finding a program 13 years out of production). Newer Macs can use MySql. If your platform is not included in the list here (http://dev.mysql.com/downloads/mysql/6.0.html), then you cannot use MySql.
Facebook is using MySQL with memcached. Most of the times it depends on the application and the requirements. One database may be good for one reason and the other for 2nd reason. First you have to analyze your requirements and then look for the suitable database. Oracle is good and no doubt about it. Can you afford to buy it?
well it depends. if your site will have small databases use mysql. if your sites have large databases similar to myspace,youtube like you said i recommend oracle but it's very expensive. However I've changed from oracle(because it was to expensive) to mysql 5.1 (you can use partition starting this version) and the difference is not so big as it was before. I have to mention that my database has 20 gb and has around 70 milions rows. My opinion. if you don't have lots of money to spend but you need large databases you should try mysql 5.1 and partition and optimise your table. if you have lots of money you should try oracle.
If firebird is a database, there probably is no reason it can't be used as a web database, although it might take more work than something that is commonly used.