What are you want with PC a complete PC or only a motherboard. If you want a complete PC then you can use nearly any model from the last 3 years, they all should be fast enough for this purpose.
If you want a motherboard, then a fanless board with standard Ramboards is good. The AsrockASR Q1900B-ITX or any similiar board is more than enough. A atom board with 2*1,86GHz is good as well. If you prefer AMD, than thats no problem, the linux version you need can run on both platforms.