The Raspberry Pi is a tiny computer that will run Linux and sells for an amazingly low price. The main site is http://www.raspberrypi.org and there's a very good magazine at http://www.themagpi.com. There's an excellent user community. All of the above make it the best tiny computer available.
The Pi runs a lot faster if you run from an external hard disk. This procedure works well. It helps to use a decent hard disk. The first time I tried I used an old PATA disk and I couldn't get it to boot. With a SATA drive and a decent SATA to USB controller everything worked with no problems.