I would suggest just trying Ubuntu first. It is the most straight forward to use and install, and I have found it supports a wider array of plug-n-play hardware than other distros. Also, because it uses Debian packages, you will have a larger library of software to choose from (vs distros not using Debian packages, like Red Hat or Fedora), and the APT package manager works very well and is easy to use. I have also found the PCLinuxOS works well with a lot of different types of hardware and is very easy to use.
If you would like to use MythTV (Linux only)as your UI, check out Mythbuntu. Also, XBMC can be used as a front-end to a MythTV backend. This means you could have a Windows based front-end for your Linux back-end/server.