I'd agree with some others here, that installing and actually using a *nix machine is a good place to start, if you want to get into *nix administration. Even trying to host a simple FTP server will be a pain if you've never spent time with the systems.
If you have to choose, I'd advocate installing and using a linux distribution, rather than buying a Mac. Don't get me wrong; I have nothing against Macs, but I've seen a LOT more linux servers than Mac servers. And I'm sure whatever client you're working with will appreciate you setting up a server with a free OS.
As others have mentioned, Ubuntu is a great distribution to play with, if you've never used Linux before. Once you've spent some time with Ubuntu, feel free to try out some other distributions, like Ubuntu Server Edition or Fedora. Oh, and make sure to back up your data before repartitioning your hard drive and installing Linux. That's important.
Once you are comfortable using Ubuntu (or whatever you install), one of the first things you're going to need to do is learn a few basic command line utilities. This article from Oracle is a great place to start. If you want to learn a few more details, they have more articles in their series.
If you ever run into troubleshooting issues running Linux, use the support forums. They are an invaluable resource. If you want some more formal reading (which you will), try Essential System Administration or Linux Administration for Beginners. I think both will be much cheaper and more up to date than some of the other books listed here.
If you want to learn how to host a web server on a *nix machine, I would definitely recommend learning about system administration in general. Sure, you don't need to know how to set up a cron job to host a web server, but it will make your life a lot easier in the long run.
Other Details
There is a partitioning tool available within Windows Vista and Windows 7 (and XP too?) that lets you repartition your hard drive. In Windows XP, you can find the partitioning tool at Start Menu > Control Panel > Administrative Tools > Computer Management > Storage > Disk Management. Make sure you are viewing the Control Panel in Classic View. Once you've opened Disk Management, just right click on your main partition, and (after backing up data!) shrink your main partition. Now you've got some room to install Linux.
To install most Linux distributions, download the appropriate .iso file, burn it to a CD, and boot off the CD. Use a program like ImgBurn to burn the file to a CD. From there, the installation is pretty simple. Install Linux on whatever space you freed up earlier, while resizing partitions. If you notice Linux creating both a swap partition and a regular partition, don't worry; that's totally normal (Windows makes a swap file, Linux uses a swap partition).
You'll find there is a 32 and 64 bit edition of almost all the distributions mentioned. The 32 bit editions tend to be slightly more compatible with certain hardware and programs; the 64 bit editions take advantage of your hardware much better. For example, I run the 32 bit version of Ubuntu on my desktop, because there is (unfortunately) only a 32 bit driver available for the wireless card in it. Also, Amazon only offers their MP3 downloader program (lol), necessary to buy music from them, for 32 bit distributions. On my laptop, I run a 64 bit distribution, as it is much more able to take advantage of my limited hardware.