a couple clarifications...
-- Oracle Express Edition versus Oracle database
if you just want to have an Oracle instance to learn the basics of Oracle the XE edition (currently only 11g) is your best choice, indeed
however the full versions of Oracle can also be downloaded for free from Oracle's download page ( http://www.oracle.com/technetwork/database/enterprise-edition/downloads/index.html )
you merely have to create a (free) account with Oracle
if you want or need to familiarize yourself with "the real thing", this is the way to go
mind yourself, patches & official support from Oracle require a paying license (http://metalink.oracle.com/ ) but for XE the forums maybe helpful ( http://www.orafaq.com/wiki/Forums )
Google & the freely provided / accessible doc are your friends ;)
-- MySQL only for "small databases" ?!?
Facebook, small? i don't think so ( http://www.mysql.com/customers/ )
thus if you just want to get familiar with Database and don't aim at becoming an "Enterprise guy", MySQL is just as good an option. possibly even better, as small companies are more likely to use MySQL then Oracle.
and any database nowadays supports Java & C/C++
SQLite is cute, but mostly used on mobile platforms (Android, Qt aso.)
well, Firefox uses it on all platforms as well, as a matter of fact
it is commonly used as "registry" replacement by many softwares; thus may come in handy for (software) development