Welcome to LQ. As you probably know, all Linux is pretty much the same at the kernel level, but everything changes by the time it is a full distribution. Questions are always welcome, although when it comes to TV, I will not be answering any of them.

Mythbuntu is probably your best bet, but probably any major distribution will work. Incidentally, Red Hat is a commercial distribution these days (it includes support, but is also quite expensive), so Fedora is the place to focus for the open source version. Good luck in any case.