We propose an effective whole-body MPC controller for locomotion of humanoid robots. Our method generates motions using the full kinematics, allowing it to account for joint limits and to exploit upper-body motions to reject disturbances. Each MPC iteration solves a single QP that considers the interplay between dynamic and kinematic features of the robot. Thanks to our special formulation, we are able to perform a feasibility analysis, which opens the door to future enhancements of functionality and performance, e.g., step adaptation in complex environments. We demonstrate its effectiveness through a campaign of dynamic simulations aimed at highlighting how the joint limits and the use of the angular momentum through upper-body motions are fundamental for maximizing performance, robustness, and ultimately make the robot able to execute more challenging gaits.