PAINESVILLE, Ohio — Mary Ann Froebe stood feet apart with knees slightly bent and aimed the .22-caliber Ruger semiautomatic. “You’ve got some adrenaline running through you right now,” said Esther Beris, the coordinator of the northeastern Ohio chapter of A Girl and a Gun Women’s Shooting League. “It’s O.K., just relax.” Ms. Froebe, 42, a small-business owner who described herself as a “virgin gun shooter,” concentrated and pulled the trigger. “It was awesome,” she said, her face flushed, after emptying the 10-round clip. “The sense of control, of being in charge of me.” In the debate over firearms regulations, the...