Jim,
The Linux medai center you're talking about, that's a MYTH TV box? Do you already have on or are you looking into getting/building one?
Either way you can choose video cards that suit your application.
I would not worry so much about the HDMI/DVI issue.
Convertors are easy to find and not expensive
http://www.ramelectronics.net/html/DVI-HDMI_adapters.html
If the Linux Media Center is set up to do component out I'd go that route.
There is a lot more involved in the "HDMI is the best" debate than simply the cable.
This is a very informative read on the subject.
http://forum.ecoustics.com/bbs/messages/34579/122868.html
Scott