[kruffin]

You'll want an Arduino that has headers and a usb connector already soldered on and the usb cable to fit it. That's really the bare minimum. From the article, this one looks like it would fit: https://www.sparkfun.com/products/11575 and only $9 on sale day.

Now if you want it to do something you can see other than in the logs from within the IDE, that's when you start needing more stuff. Generally a breadboard, wires, and some components like leds and resistors come next; for making blinking lights, who doesn't like those?

As far as the computer, it can be best answered here but is just about anything you have: http://arduino.cc/en/Guide/HomePage in the getting started section.