I just put together a couple of systems, I don't use JRiver to play the media but the concepts are the same.
CPU - For single purpose events like playing a single blu-ray movie at a time, ghz is way more important than the number of cores.
Video Card - I am playing movies thru a Nvidia onboard 9400 and they play fine, just a dropped frame (stutter) on a very rare occasion, higher end card would be better I am sure
Memory - 4gb would be the minimum, though memory once again isnt that big of an issue, the 1st two items make the big difference
Case - I have a micro case and love it, if it is going to be sitting by a HDTV or speakers, make sure you build it quiet.
Hard Drives - Solid state drives will offer you no real advantages in playing media over regular drives.
If you are serving your movies over a network, make sure that you are running 1GB ethernet or above, 10/100 isnt going to cut it.
These are my opinions only, hope something helps, do your research and ask others before building your system.
TC