The quickest way to learn the Unix, or more likely Linux, would be to dive in head first. First off, try to install a Linux distro from scratch (preferably without a GUI). Once it is running, customize and explore. Before you can learn anything too in depth about security, you have to learn more about the structure, file system, and processes connected with the OS. Some of the better flavors of *nix are Gentoo, Debian, Slackware, and my personal favorite, *BSD (OpenBSD, FreeBSD, NetBSD). FreeBSD has a GREAT handbook for it that is available all over such as
here. It is in virtually every language and seems to be the best maintained documentation of the *nix flavors. In addition, the BSD's are the closest thing to unix you will get running on an x86 machine.
http://linuxiso.org/ is a great place to find all the *.iso images needed for installing a linux distro, as well as the *nix's homepage.
I forgot one other flavor. I hate it, but others seem to like it a lot. Its called Knoppix STD or something like that. It is a single CD that boots from the CD, no installing necessary. You just lose some functionality.