I agree with some others here that installing and actually using the * nix machine is a good place to start if you want to go into the * nix administration. Even trying to host a simple FTP server will be painful if you have never spent time with systems.
If you need to choose, I would recommend installing and using a Linux distribution rather than buying a Mac. Do not misunderstand me; I have nothing against the Mac, but I have seen LOT more Linux servers than Mac servers. And I’m sure that any client you work with will appreciate setting up a server with a free OS.
As mentioned, Ubuntu is a great distribution if you've never used Linux before. After spending some time with Ubuntu, feel free to try out other distros like Ubuntu Server Edition or Fedora . Oh, and be sure to back up your data before remaking your hard drive and installing Linux. It is important.
After conveniently using Ubuntu (or what you install), one of the first things you will need to do is to learn a few basic command line utilities. This article from Oracle is a great place to start. If you want to know a few more details, they have more articles in their series.
If you run into Linux troubleshooting problems, use the support forums . This is an invaluable resource. If you want a more formal reading (what you will do), try Essential System Administration or Linux Administering for Beginners . I think both of them will be much cheaper and more relevant than some of the other books listed here.
If you want to know how to host a web server on a * nix machine, I definitely recommend that you learn about system administration in general. Of course, you do not need to know how to configure the cron job to host the web server, but in the long run it will make your life a lot easier.
Other information
Windows Vista and Windows 7 (and XP too) have a partitioning tool that allows you to remake your hard drive. In Windows XP, the partitioning tool can be found in the Start menu> Control Panel> Administrative Tools> Computer Management> Storage> Disk Management. Make sure you are viewing the control panel in Classic View. After you open Disk Management, just right-click on your primary partition and (after backing up your data!) Change the primary partition. You now have a place to install Linux.
To install most Linux distributions, download the appropriate .iso file, burn it to a CD, and download it from the CD. Use ImgBurn to burn the file to a CD. From there, the installation is quite simple. Install Linux on any space that you previously freed up when resizing partitions. If you notice that Linux creates both a swap partition and a regular partition, don't worry; which is completely normal (Windows does the swap file, Linux uses the swap partition).
You will find a 32 and 64-bit edition of almost all the distributions mentioned. 32-bit versions are generally slightly compatible with some hardware and software; 64-bit versions greatly enhance your hardware. For example, I run the 32-bit version of Ubuntu on my desktop because it has (unfortunately) only a 32-bit driver for the wireless card. In addition, Amazon offers only its MP3 (lol) download program, which is required to purchase music from them, for 32-bit distributions. I am running a 64-bit distribution on my laptop, as it is much more capable of using my limited hardware.