At the end of the day, to follow this tutorial, along with the supplies you already should have (M-F jumpers, breadboard, Raspberry Pi), you will also need an H-Bridge (L298n), four motors, power for the motors, and some sort of frame. I went ahead and just bought a kit for simplicity, but this is extremely open-ended. The same motors I used can be found on ebay very easily. Just type in Raspberry Pi motors. They are cheap and weak. Feel free to hunt for something better.
In order to achieve true wire-less, you will also need a wifi dongle (search for "edimax wifi") and some sort of power supply. The Raspberry Pi wants 5v ~1000mA. Since we use cell phone chargers, it only makes sense to use a portable cell phone battery pack. I used an ankur pencil charger, which provided plenty of power. Use whatever you like.
Frame/wheels that I bought:
These two together:SainSmart 4WD Drive Aluminum Mobile Robot Platform for Robot Arduino UNO MEGA2560 R3 Duemilanove *Silver*
+SainSmart L298N Dual H Bridge Stepper Motor Driver Controller Board Module for Arduino UNO MEGA R3 Mega2560 Duemilanove Nano Robot
Or you can just buy:SainSmart Mobile Car Kit with Sensor Shield V5 + 4WD Mobile Platform + Dual H Bridge Stepper Motor Driver + HC-SR04 Ultrasonic Distance Sensor + UNO/UNO R3/Mega2560/Mega R3(optional) for Arduino (UNO, Silver)
The wifi dongle:Edimax EW-7811Un 150Mbps 11n Wi-Fi USB Adapter,Ideal for Raspberry Pi
Portable cell phone charger for external Raspberry Pi power:Anker(R) 2nd Gen Astro Mini 3200mAh Lipstick-Sized Portable Charger