This hat is based on the corrugated rib stitch popularly used in waistbands and wristbands of Fair Isle type sweaters. You knit one color and purl the second color so the stitch forms a double layered fabric that does not curl and is much less stretchy than most ribbing. This would be a good time to learn two handed stranding - I usually do the knit stitches Continental (pick) and the purls English (throw.) There are also a few basic cable stitches.
You’ll need about 100 yards each of two colors. Suitable for worsted or aran weight yarn.