In general, I'd recommend normal grip for a multitude of reasons, the primary being, activation of your muscular chain. (barbrothersgroningen.com)
The study showed that elevated systolic blood pressure (150 or greater) and diastolic blood pressure (90 or greater) correlated with a substantially higher likelihood of dying for those with normal grip strength, which is 26 kilograms or more for men and 16 kilograms or more for women. (sciencedaily.com)
The Perfect Fitness Multi-Gym Doorway Pull Up Bar has three padded grip positions for hammer grip, close grip, and normal grip pull - ups. (businessinsider.com)