Any distribution would suit; you probably want to approach it from the point of view of "which distro is easiest to configure and manage if I don't know what I'm doing?".
Fedora/Ubuntu seem to be good beginner choices. Slap WEBMIN upon either to configure it remotely via a web page (don't actually need to have a web server running first; webmin has its own server). Add SAMBA to turn it into a file/print server, configure that via webmin. Networking should already be installed; again configure firewall/routing/traffic shaping/etc through webmin.
I'd also advise running the server in "headless" mode - drop the run-level down to disable the graphical desktop - to conserve resource if you're performing all management through webmin.
An alternative is to look at some of the many media players around, for instance the
XBMC project - it started as a hacked OS to drop onto the XBox to turn it into a media centre, then became a separate media centre in its own right (xbox no longer a requirement).
MythTV is also a popular choice.
Maybe even a distro that's closer to Windows Media Centre, ie: the distro itself is purely media centre software, rather than a platform to install media software upon:
MythBuntu is essentially Ubuntu + MythTV together, turning a PC into a stand-alone HTPC.
The advantage of the latter is that any quirks between OS and SW have been sorted out, and most Debian/Ubuntu/Mint users know how to dabble with the underlying OS to append additional functionality above and beyond MythTV without breaking the media part.
The last bit of advice I can give is:
- run this as a project. Form a "requirements document", a kinda checklist of what you're after.
- see how long/easy it is to tick those off under Fedora. Then try the same under Ubuntu. Then MythTV, etc.
- gain experience of using each system, evaluating the benefits of each, weighing them up against what you've already tried (I know many people who spend a great deal of time attempting to do everything under one distro without look at alternatives - once they've started, they continue to dedicate a LOT of effort into proceeding with the hard route rather than consider going back and starting again down an easier path).
- treat your first installs as disposable and experimental, rather than the "finished product".
- once you've finished playing around with the system available, you can begin planning for the "real thing".
The drawback with this approach is the amount of time and effort you need to initially invest. The advantage is that you'll become pretty experienced with the alternatives, will have greater familiarity with the system you're now using, and can use it to its maximum benefit. Investing in the time and effort at the start means greater rewards in the long run - scrimp on this and the ongoing journey can be quite daunting and arduous.
