The three fibres that matter for beginners
Acrylic
Acrylic yarn is where most beginners start, and for good reason. It is cheap (a 100g ball costs £2-4), machine washable, widely available, and comes in every colour imaginable. It is forgiving to work with because it has a slight stretch that keeps your tension even. The main downside is feel: acrylic can be squeaky against the hook and some people find the texture plasticky compared to natural fibres.
For learning stitches, making practice swatches, and completing your first few projects, acrylic is the right choice. You will make mistakes and you will frog (undo) your work multiple times. Expensive yarn makes those mistakes feel expensive too, which is the last thing you need when you're learning.
Cotton
Cotton yarn produces a crisp, structured fabric with excellent stitch definition. You can see every stitch clearly, which is helpful when you're learning to count. Cotton doesn't stretch, which means your tension needs to be more consistent. This makes it slightly harder for absolute beginners but excellent once you have basic stitch control.
Cotton is the standard choice for dishcloths, market bags, amigurumi, and summer garments. It handles water well, it doesn't pill, and it softens with washing. Mercerised cotton (cotton that has been treated for a slight sheen) is especially pleasant to crochet with. Scheepjes Catona and Paintbox Cotton DK are both excellent and affordable.
Wool
Wool is the traditional crochet and knitting fibre. It is warm, elastic, naturally water-resistant, and has a beautiful drape when worked up. Superwash wool (treated so it can be machine washed without felting) is the practical choice for wearable items. Pure wool that hasn't been superwash-treated will felt if you wash it in a machine, which is either a disaster or a design feature depending on your intentions.
For beginners, wool is a second or third project fibre rather than a first. It costs more than acrylic, it requires more care in washing, and some people find it itchy against their skin. But once you're comfortable with the basics and want to make something that feels genuinely luxurious, wool is worth the step up.