I agree with the comment about finding a position where you can do Unix plus other stuff. I started with a help desk position where I did Windows, Netware, OS/2, and Unix all. Since I liked Unix and knew it best of all the help desk guys I was able to work my way into a Unix admin position after a while.

Also, check out The Practice of System and Network Administration by Limoncelli and Hogan. It has tons of material about finding sysadmin jobs and beign successful once you have them.