I want to build a small network and security appliance (server) based on a fast Intel Atom CPU. What I need is an Atom CPU (or similar), minimal RAM (1GB is more than enough), a USB drive or SATA Disk On Module (for a small system image), and Gigabit Ethernet. The dimensions of the board aren't important. ARM CPUs are too slow. Most importantly, I don't want lots of multimedia and other interfaces which I feel uncomfortable with for robustness and security reasons. What I'm looking for is something specialized like the Parallela board but for Atom. I am running basically XEN so the CPU should support virtualization. On top of XEN will be MirageOS.
You might be interested in the APU boards from PC-Engines. I'm using one for my home-spun router. You get 3 Gig-E interfaces, a dual-core AMD CPU that appears to support virtualization, 2 or 4 GB of RAM, and SD card/mSATA/USB boot capability. You use a serial port to access the system console, and there's no multimedia to speak of.
Here in the US I ordered my board from Mini-Box. The 4GB model is $169.
Mini-box also carries enclosures and the like to go with it. It uses a standard 12V barrel plug power supply - the same kind that comes with many routers, external hard drives, etc. You may even have one lying around. (I did.) For the serial console, you need a null modem cable and maybe a USB-to-serial adapter depending on what else you have lying around. Putty works great as a serial console app.
The AMD CPU has performance roughly comparable to Intel's "Bay Trail" Atom series. It's fully x86-64 compatible and runs Linux well.