Welcome to LQ!
I would suggest Debian (but then, I always suggest Debian...

).
Add the debian-multimedia repositories, and install MythTV. You will want to use Debian Testing though.
I have a guide
Here that may be useful. Some of it is Aussie specific, and some is TV tuner specific, but it should still point you in the right direction for most of it...
I hope this helps
--Ian