Design of robotic grippers for a target-object family is currently hand-tuned and expert-driven, with a tight and necessarily co-tuned relationship between finger geometry and grasp control strategy, and with candidate geometries typically evaluated by means of time-consuming contact-dynamics simulation. Automated systems, if they have existed, have generally been either geometry optimizers, often with a pre-set body control law, or jointly designed body and control for single-object performance. The design of both geometry and control together, with a WTC-metric for reliability, has remained unposed. Here, we detail a decision-support system which automatically recommends the Pareto-optimal set of designs for a group of target-objects according to several simultaneously competing objectives by simultaneously choosing the finger geometry and the grasp control strategy. It combines contact dynamics simulation with an expected-hypervolume improvement active learning strategy searching over the design-and-control space using a surrogate and explicitly incorporates grasp reliability into the objective and provides a confidence diagnostic of the control-optimality-gap. The results from a multi-object, multi-shape grasping task run in MuJoCo software over 10 random seeds match or exceed current benchmarks for dominated hypervolume and inverted generational distance, achieving the highest score for those and the most evenly distributed front. Using its best possible fixed control (via grid search) when a design-only system is employed as a baseline, geometry-only optimization achieves an identical result in the final dominated hypervolume of the Pareto front to this system (1.40, compared to 1.40 and Wilcoxon p=0.86), showing no statistical advantage to the system in final hypervolume (no significance after Holm-Bonferroni correction, previous significant gap achieved from inappropriate fixed control), while achieving best-in-class results in term of automatically generated fronts, front quality, and sampling efficiency, in addition to the explicit confidence diagnostic for the control-optimality-gap and robustness measures. The performance reported is achieved in a simulated numerical investigation.