This article tackles the problem of designing 3D perception systems for robots with high visual requirements, such as versatile legged robots capable of different locomotion styles. In order to guarantee high visual coverage in varied conditions (e.g., biped walking, quadruped walking, ladder climbing), such robots need to be equipped with a large number of sensors, while at the same time managing the computational requirements that arise from such a system. We tackle this problem at both levels: sensor placement (how many sensors to install on the robot and where) and run-time acquisition scheduling under computational constraints (not all sensors can be acquired and processed at the same time). Our first contribution is a methodology for designing perception systems with a large number of depth sensors scattered throughout the links of a robot, using multi-objective optimization for optimal trade-offs between visual coverage and the number of sensors. We estimate the Pareto front of these objectives through evolutionary optimization, and implement a solution on a real legged robot. Our formulation includes constraints on task-specific coverage and design symmetry, which lead to reliable coverage and fast convergence of the optimization problem. Our second contribution is an algorithm for lowering the computational burden of mapping with such a high number of sensors, formulated as an information-maximization problem with several sampling techniques for speed. Our final system uses 20 depth sensors scattered throughout the robot, which can either be acquired simultaneously or optimally scheduled for low CPU usage while maximizing mapping quality. We show that, when compared with state-of-the-art robotic platforms, our system has higher coverage across a higher number of tasks, thus being suitable for challenging environments and versatile robots. We also demonstrate that our scheduling algorithm allows higher mapping performance to be obtained than with naïve and state-of-the-art methods by leveraging on measures of information gain and self-occlusion at low computational costs.