This paper presents algorithms for optimal selection of needle grasp, for autonomous robotic execution of the minimally invasive surgical suturing task. In order to minimize the tissue trauma during the suturing motion, the best practices of needle path planning that are used by surgeons are applied for autonomous robotic surgical suturing tasks. Once an optimal needle trajectory in a well-defined suturing scenario is chosen, another critical issue for suturing is the choice of needle grasp for the robotic system. Inappropriate needle grasp increases operating time requiring multiple re-grasps to complete the desired task. The proposed methods use manipulability, dexterity and torque metrics for needle grasp selection. A simulation demonstrates the proposed methods and recommends a variety of grasps. Then a realistic demonstration compares the performances of the manipulator using different grasps.