It does matter. There are pros and cons to each different driver setup.
If you wire the motor as a bipolar, which I'm not sure that you can, you can use the driver that you linked, but it is not very good for driving stepper motors. https://www.sparkfun.com/products/11876 is a better driver for steppers for half the price. (still have to wire it bipolar)
If you need to stick with unipolar wiring, PCBheaven.com shows an example using a CD4017, MOSFETs, and diodes to run a unipolar motor. It will only turn one direction. Instead you could use a micro-controller, such as an Arduino, in place of the CD4017 along with logic-level MOSFETs to go both directions.
A tutorial on the Arduino site uses a ULN2003A, which is not powerful enough to drive your motor to its full potential (does it need to turn, or turn well?) and doesn't have the diodes (important to protect your IC!), but the Arduino sketches would still work using the schematic from PCBheaven.
A couple of complete driver boards:
UNIPOLAR STEPPER MOTOR DRIVER
FANCY UNIPOLAR STEPPER MOTOR DRIVER