Twenty-some years ago, I took an Intro to Art Therapy course. Art therapists use a variety of media with their clients, the selection based not only on the client's age, but also on their presentation and the outcome the therapist is trying to elicit. I love to draw, and have found that different media work better for different moods. The following is based on my own experience, not any scientific data.
My favorite drawing medium is colored pencil. I like it because the effects you can get are infinite, smooth/textured, light/dark, bright/pastel, etc. It is a medium that can be used quickly, but getting the richness and detail that characterize colored pencils takes patience. My drawings cover the page fully with color, they are not line drawings. I shade one color into the next, and often blend them with a white pencil or a colorless blender. I like colored pencil for almost any mood, but some people might find them frustrating if they are angry, anxious or antsy. When I am drawing with colored pencil, I can really get 'into the zone', focused to the point of mindfulness or meditation. This helps distract me when I am hurting.
I work on two inpatient psych units at a hospital. We always keep a supply of pictures for the patients to color, along with markers and crayons. People often think of coloring as an activity solely for children, but it is appropriate for anyone. It can help a person focus, relax, and occupy their hands and mind when feeling anxious, antsy or depressed. Crayons and markers can both give good color. Fine tip markers can be used for detail, it can be hard to get much detail with crayons.
When drawing rather than coloring (drawing being making your own images, coloring is adding color to a supplied image), both crayons and markers can be very expressive. Crayons can be good for freeing yourself, because they are associated with childhood, before we were told all the rules of how a drawing is 'supposed' to be. Markers are more vivid. If I am feeling confused or out of sorts, I sometimes take a large piece of paper and either markers or crayons, and just let myself draw without thinking or planning. As lines, shapes and colors appear, I often can relate the drawing to myself and my situation, and find some answers, or at least understanding.
Pastels and oil pastels are fun because they lend themselves very well to blending and shading colors. They can also be messy, which can be frustrating, or it can be part of the art experience, depending on your viewpoint. Chalk works similar to pastels, but the colors of pastels tend to have a greater range, where chalk tends to be more pastel (go figure). Crayons, pastels, oil pastels and chalk can all be used easily to cover a large area with color, by peeling off the paper covering (if there is one), and using the side rather than the tip. This can be used to express more intense feelings like anger or joy, which don't have the patience for fine detail. Pastels also come in pencil form, which can give good detail like colored pencils, for when you are calmer.
I hope this inspires you, and gives you some ideas. You don't need to be an artist to enjoy putting your marks on paper. Art can also be used to release and express emotions. Get some paper, and experiment with different media. Find what feels right for you. You might discover you are an artist, after all. Art is in the eye of the beholder. No one else has to like it or understand it.