The darlington array (for a unipolar) or h-bridge (for a bipolar) will work just fine for basic functionality, the A3977 just gives you much smoother operation, as it can do 1/8 micro stepping. You can decide of this is necessary depending on your application.
I have only recently started my electrical engineering classes also, and have begun working in lab, and am just as excited to you to see this whole new world opening up before me. It really is amazing. I have begun to think of small projects for this that I can make to simplify menial tasks around the house. It feels good to be able to harness science and exploit it for my benefit. I have a LOT to learn, but that is an exciting prospect to me.
Keep me posted on your progress, and please share any cool tips and tricks that you learn.