You will need to first decide what kind of mountain climbing you will be doing, and in what conditions, before choosing the best gear for mountain climbing. Much of the gear for mountain climbing will be fairly expensive as well, so you will need to prepare a budget for the gear you will need. Be sure to choose a high-quality harness, waterproof and breathable clothing, and all necessary safety equipment such as a helmet, goggles or glasses, gloves, and so on. If you are new to the sport, it is a good idea to consult a professional guide or a store that stocks such equipment.
The best gear for mountain climbing will be lightweight, functional, and durable. You will need a harness that should fit snugly but comfortably. The harness should be adjustable so you can wear it while wearing other layers of clothing, and it should feature plenty of gear loops from which you can hang carabiners and other equipment. Carabiners are hooks with closing gates that will allow you to connect pieces of gear during the climbing process. Some carabiners feature locking gates that prevent the gate from opening during use, while others do not. You will more than likely need several of both models, so be sure to stock up on these carabiners, as they are multi-functional and easy to store.
Other pieces of gear for mountain climbing are designed to keep you warm and dry during inclement weather. It is best to dress in layers; be sure to choose clothing that is breathable, as such clothing will wick moisture from sweat away from the body, keeping you warm and dry during physical activity. Outer layers should be waterproof and breathable, keeping snow and rain moisture away from the body while still allowing moisture from sweat to escape the outer layer.
Ice axes and crampons are important pieces of gear for mountain climbing, and it will be necessary to choose axes and crampons that will work well for the specific purposes of your climb. Ice axes in particular are designed for different applications, from mountain climbing to vertical ice climbing. Some ice axes feature a straight shaft, while others have a bent shaft, and the pick attachments can vary as well. It is best to consult an expert to determine which type of shaft you will need, as well as which type of pick attachments will be most appropriate for the mountain climbing you will be doing.