If you get sufficient RAM, you don't need to worry about onboard nVidia chipsets and shared memory. Again, if you have the option from the beginning you want to go with nVidia. ATI is a problem under Linux, generally, and under LinuxMCE specifically. You might be able to get it working... after much crying and gnashing of teeth,... but you'll wished you hadn't. Before ATI, I would say to go with an embedded Intel chipset (other than the GMA500 or GMA600, PowerVR chipsets that don't work right in Linux). Intel chipsets in the GMA945 or its successors will be a good 2nd choice from nVidia chipsets.
The conflict between the HVR-1600 and the nVida chipsets is a somewhat well known. See here:http://ubuntuforums.org/archive/index.php/t-1043884.html
Blueray support may not be there
yet... I've taken a pass on blueray until it's better supported in Linux generally. I don't like the idea of re-purchasing all my media because of blueray, or getting a bunch of 4TB drives to store it all, either.