As you might suspect, your hardware platform will begin with two DC motors and two wheels. You'll also need a simple hardware set to which you can attach your motors and wheels. You can either purchase pieces, or an entire kit, such as the one offered at http://www.sainsmart.com/sainsmart-balancing-robot-kit.html.

If you are buying pieces you'll want to start with two DC motors with encoders, such as the 9.7:1 Metal Gearmotor 25Dx48L mm LP 6V with 48 CPR Encoder available at http://www.pololu.com or http://www.amazon.com. You'll also want wheels that fit these motors, both http://www.pololu.com and http://www.amazon.com have these as well.

You'll need some acrylic parts that allow you to attach the wheels as well as the battery and Raspberry Pi. Here is an image of the kit parts assembled with the motors and wheels. You can certainly cut your own parts from acrylic. Either way, here is the completed basic platform:

Now you'll need to add the electronics.