Easy Ribbed Headband
This is the one I'd hand a friend who wants to learn crochet. It's a beginner friendly ribbed band worked entirely in half double crochet, and that cozy ribbing comes from working into the back loop of every stitch. You can make it as wide or as narrow as you like, so it's easy to get the fit just right.
It uses worsted weight (4) yarn and a 4.5 mm hook, so it grows quickly and stays nice and stretchy. You crochet a flat strip to fit your head, then join the two ends with a row of slip stitches to close the loop.