Process
I researched a wide variety of stitches. The most popular option, aside from the single chain stitch, seems to be the double chain stitch. Of course, there are a multitude of variants on the basics, such as the half double crochet stitch and the triple crochet stitch.
Though one can spend hours looking up infinite kinds of stitches, after a certain point it becomes much easier for the eye to pick up the primary differences between stitches.
Choosing certain stitches over one another really boils down to two things: density and appearance. For example, double chain stitches make for firm but flexible material, making them a popular choice for sweaters. The single chain stitch results in an incredibly dense weave, which doesn't lend itself quite as well to making a comfortable sweater.
While the fancier stitches, like the cable crochet stitch or even the braided cable crochet stitch, seem quite daunting for a novice like myself, I decided to at least experiment with changing the density of the yarn I used with a single chain stitch from the thinner kind we used in class to a thicker, woolier yarn.