Since climbing is not just climbing, this question also has slightly different answers depending on the discipline. Comfortable clothing, climbing shoes and a chalk bag are sufficient for indoor bouldering in the climbing hall. If you want to try a via ferrata or sport climbing in Ötztal or even ice climbing, you will need significantly more equipment. The basic gear includes climbing shoes, climbing harness, climbing helmet, climbing rope and belay devices as well as chalk bag and chalk, quickdraws, slings and carabiners.
A light backpack with snacks, enough to drink, sun protection and an extra layer of warm clothing are an absolute must on longer climbing tours. When choosing the climbing pants and shirt, just follow your preferences - it should be breathable and ready for use according to the onion principle. The packing list for ice climbing is even longer and includes, for example, crampon-compatible mountain boots, crampons, ice ax, ice screws and warm clothing.
What makes all climbing equipment really complete is motivation and a good mood!