I just installed XBMC on the Celeron Chromebox. A piece of cake to install and it runs beautifully. I think that fits in the sweet spot you're looking for.

I prefer the Asus Chromebox. It is 69$ more than the Amazon Fire TV but it has much better specs:

-Intel Haswell architecture instead of ARM CPU (good difference in term of performance)

-16 GB SSD internal storage instead of 8 GB

-Ethernet 10/100/1000 instead of 10/100

-Intel HD 4000 instead of Qualcomm Adreno 320

http://www.amazon.com/Asus-CHROMEBOX-M004U-ASUS-Desktop/dp/B00IT1WJZQ