In the description they say that you can run the pump as if it were a stepper motor. This seems like it could be done perfectly with an Arduino, but I was not sure whether to treat it like a Unipolar or Bipolar stepper motor as the setup for each is quite different. Does anyone have any thoughts as to which it might be? Thanks so much.
Between the brushed DC motor, brushless DC motor, and stepper motor the stepper motor is the best choice. The other two options won't give you any precision in control. Well, the brushless DC motor might but you'd be building your own motor driver which is not a simple task...
This A4988-based driver for bipolar steppers is very popular (especially with RepRap-style machines) and should work well for you. You can find plenty of examples on the web, but the gist of it is that every time you toggle the "STEP" pin high it will rotate your pump motor 15 degrees.
On the driver board there's a small potentiometer which needs to be adjusted to 250ma current per this pump's maximum current. See the instructions for details. If you drive the motor with too much current it will overheat (feel the motor with your fingers to make sure it doesn't). A 5V supply should be OK, but if you can't get it to spin quickly enough you can use up to a 35V supply.
The AccelStepper library will make interfacing with the driver pretty straightforward.
The H bridge would be used with the brushed DC motor option. It would not offer the precision of RPM that the stepper motor option provides.
...well, if you like doing things the hard way, you could use a couple of those and build your own stepper driver but it would be a complex, inefficient, pain in the butt. The A4988 driver is without a doubt the better solution.