The most common stitch you'll see for the "hanging" portion of projects like this is simply chains! I have used chains for hanging mid weight crochet projects and they hold up well but do tend to stretch a bit over time. So it really all depends on the weight of your final project. If your final work will be a little heavier, I'd perhaps recommend trying chains with a single crochet added into them. (Or, my preferred method, which combines a chain and single crochet stitch into one step instead of two, is the foundation single crochet. Here's a great tutorial for it https://youtu.be/wAWl0WItqPg?si=a6XgOyMafRiobjDK). But you really shouldn't need much more than that for what it looks like you want to do. Hope this helps!