Is that the same motor they have in SAIC’s Resale?
While you could certainly get the dedicated driver chip (they have some advantages) for a really cheap and easy start, you might consider a collection of Mosfets+Diodes, TIP+Diodes or a Darlington Array along with the built-in
Stepper functions in Arduino.
We carry the ULN2803 Darlington array in resale for $0.50 or so. The TIP and mosfet transistors are also available. Basically the Darlington array is like using 4 TIPs or Mosfets (plus their diodes) all in one small package.
If you go that route and you’re willing to document your process I’m happy to just give you any of those components from the class locker
That said, the Adafruit shield works great. It’s just a bit pricey and does way more than you need it to. But it may save you some time.