First off, thank you for your responses! Now, I am not sure on the exact size of the barrel yet. I haven't begun building it, but it has to launch a water balloon, so I would assume around 6" diameter. I will upload some sketches as soon as I have some.
Jackrae, it is a Telco Intercon Motor, and after doing some more digging I found a datasheet for the series, but not the exact model #. http://www.telcointercon.com/uploads/downloads/pdf/Stepper%20Motor/High%20Torque%20Stepper/4T56.pdf
It looks to me that the break down goes like this: 4T = 4 Coils 56 = Case Dimensions 18 = 1.8 degree/step M = Medium Size Length 300 = 3 Amps 8 = # of Wires
Now, I have only dealt with 4 wire motors in the past, do I have to do anything special to drive this?