Most UNIXes are commercial. Most also cost money to use.
The exceptions (that I'm aware of) are Linux, the BSDs (OpenBSD, NetBSD, and FreeBSD), and the GNU HURD.
UNIX technically refers to operating systems that have passed some kind of standard test; it takes money to pass the test, and Linux and HURD don't feel like paying, so they're really just UNIX-like operating systems. That's close enough for most people, of course. (I don't know much about the BSDs).
If you're a beginner to UNIX, Linux is probably the way to go. HURD is too unstable adn incomplete right now (and no one knows about it), and I think the BSDs are geared towards more advanced users.
Of the Linuxes, the two I posted above are supposed to be good for beginners. So is Suse, but I think its free download is an FTP install only. More advanced Linuxes include Slackware, Debian, and Gentoo.