I would prefer a wired connection to the router, but this will have to do as far as networking is concerned with how the rents how is setup.
I am leaning towards Windows 7 for an OS, but my pops would like to have something free, hence the Mythbuntu for the OS, this is really the only part that I have no idea on, I am a complete noob when it comes to setting up/installing anything linux, but I do have knowledgeable friends to assist in this area.
I feel the areas that could be cut back on are the, CPU, and Video Card at the very least. I think a 4670 would do the job just fine, but i decided to "over do it" with room to cut back.
I would spend some money on a quad core since they might be doing some encoding/transcoding with the system. An onboard is all you need for a HTPC. I would try to talk them into Windows 7. I use Windows 7 on my HTPC and it works great.
I like shorties list. I would even try to save a bit more and look at ddr2, and a 780 G motherboard. Its true that they will be able to watch whatever they want with the onboard, but I would spring $50 for an HD4650. You could easily find one that is passively cooled, although those run about $10 more.