We present a new approach to robot hand design specifically suited for successfully implementing robot learning methods to accomplish tasks in daily human environments. We introduce BaRiFlex, an innovative gripper design that alleviates the issues caused by unexpected contact and collisions during robot learning, offering robustness, grasping versatility, task versatility, and simplicity to the learning processes. This achievement is enabled by the incorporation of low-inertia actuators, providing high Back-drivability, and the strategic combination of Rigid and Flexible materials which enhances versatility and the gripper's resilience against unpredicted collisions. Furthermore, the integration of flexible Fin-Ray linkages and rigid linkages allows the gripper to execute compliant grasping and precise pinching. We conducted rigorous performance tests to characterize the novel gripper's compliance, durability, grasping and task versatility, and precision. We also integrated the BaRiFlex with a 7 Degree of Freedom (DoF) Franka Emika's Panda robotic arm to evaluate its capacity to support a trial-and-error (reinforcement learning) training procedure. The results of our experimental study are then compared to those obtained using the original rigid Franka Hand and a reference Fin-Ray soft gripper, demonstrating the superior capabilities and advantages of our developed gripper system.