I have helped several people to learn UNIX. One of the best ways to do this is "Hands On". Unix comes in many different flavors... Sun Solaris, AIX, True 64, HP/UX, BSD, Linux etc. What you need to remember is that the syntax for commands, installation processes, volume management tools vary from flavor to flavor. It is best to pick just one and adapt to others as you progress. For a beginner I recommend starting with Linux. It is the least costly and most widely used by people who have a PC at home. It also helps to find a friend who wants to learn unix too... for example if two people work together they often learn twice as much in half the time and it also gives them more equipment to experiment on... note: it take more than one machine to set up a network. After you have learned Linux move on to a new flavor such as Sun Solaris for Intel or BSD/OS. As you land jobs in the Unix Environment you will gain access to Enterpise level Unix flavors and Platforms such as Sun's Sparc processor bases Solaris, and RISC based flavors such as AIX and HP/UX. To date I have worked with at least 7 flavors of UNIX. Remember, no one person can know all there is to know about UNIX. What matters is that we strive to learn all we can about it.
I would suggest that you install Linux at your home system and learn about the architechcture. There are pretty good books in the market that talks about the Unix. But try to learn the scriptings and some of the most common tools like vi and etc.
I would personally recomend you to read the book:
UNIX SYSTEM ADMINISTRATION HAND BOOK 3rd ED
TRENT R. HEIN