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I would recommend trying Ubuntu 8.04, as Ubuntu is a fairly user friendly Linux distro, with an easy package manager. There is a server edition available, but installing the desktop system (Gnome by default) and all other things needed upon installation are all done through the command line, which may seem very daunting and convoluted for your first install. I believe the desktop edition has a GUI installer. I, personally, have only used the server edition.
Once you have that installed, you'll need to install Samba and edit some configuration files.
Let me know when you get to that point, and I'll attempt to walk you through it. It's a bit of a pain, with a lot of tweaking, but it's very doable. IM me or post here. I will probably be in lala land at either place. (If you know how I am.) I'll try my best to check back in often.
EDIT: Here's a small suggestion. You could use the file server as a media box, as well, and connect it directly to your TV and sound system. I've done that in the past and will be doing it in the near future, whenever I can afford to put another box together.
Recommended programs:
Video player - mplayer
Music player - exaile (last.fm support), xmms
Wine - Windows implementation system. Can run some Windows programs. (However, Wine Is Not an Emulator. Just like GNU is Not Unix. {geek moment})
Mp3/Ogg tagger - Audio Tag Tool
Useful image viewer- kuickshow (great for manga, scroll wheel allows progression to next image, better than click, back, click)
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