pull up is without a doubt one of the key exercises for developing strength and size for your back muscles(like latissimus dorsi and infraspinatus) and arm(like biceps brachii, brachialis, and brachioradialis), but most people cannot perform it.
most of the time the reason is due to incorrect posture, not power. no matter what variation you do, make sure your core is activated by bringing your leg forward not back. this is going to help you have more balance during the movement and this added control is going to keep your joints healthy as well.
make sure you control the speed since this exercise uses your whole body weight and that can be detrimental if you accelerate without decelerating. there are lots of variations which mostly are based on how you position your hands.
basically, the wider your grip is, the more lateral muscles(or muscle fibers) of your back you are going to target, and the more narrow you position your hands, the more medial muscles get involved. pronating and supinating the hand is also going to affect which muscles work more. when you pronate your hand, more forearm muscles get involved, and if you supinate, more biceps brachii heads are going to be targeted(but make sure you only supinate when your grip is narrow). also letting your shoulders be elevated or depressed is going to work more on mid-back muscles while keeping the shoulder steady works more on lateral fibers.