Well.... I have a computer I call an HTPC.
It is running Linux mint. All I really use it for is streaming movies from my server, watching netflix or playing music through the receiver. I have not really messed with XBMC, Kodi so not sure what the requirements are.
The specs of my machine are:
Intel I3-4160
8gig ram ddr3 @ 2133Mhz
GTX 650 1gig ram
gigabyte motherboard - I forget what one, but it is a microATX. I could look it up if interested.
550w SeaSonic PSU Bronze
The graphics card I have has a full HDMI plug on it so I can just plug it directly into the TV. I also have some wireless controllers and most every emulator on it, like Kega and such. I can then play any steam games that use a controller and any games via an emulator.
I usually bust out my Duo for TurboGames though as I have a XRGB-mini and it looks amazing.
But... I don't think you need anything crazy, but you may want to future proof just a little. The stuff I got was cheap a couple hundred bucks to build it and the OS was free so....
I don't do any real TV as it's a waste imo. If I wanna watch something and I don't have it I rent it, slap it on my server then return it and then I can watch it whenever I want no commercials.