Can anyone recommend some hardware which meets the following criteria:USB port (more than 1 would be handy but a USB hub could always be used)Suitable for running a reasonably small Linux distribution (No GUI needed. Want to run MySQL and some other custom bits. I'm not quite sure how one goes about installing Linux and configuring on a device without a video out.)Reasonably small (thinking a small router)Low power consumption (less than 10W, ideally closer to 1W)Just a little background: I'm currently working on some home automation projects and having some USB/serial devices I want to capture data from and log to MySQL.
Recommendation for low-power, cheap, USB-capable hardware to run Linux
usb;linux
The classic device for low-power Linux usage is the Raspberry Pi.  Either the model 1 B+ or the model 2 B will meet your needs: 4 USB ports, can run headless just fine, is about the size of a deck of cards, and draws about 3W.