Propulsion of chiral magnetic nanomotors powered by a rotating magnetic field is in the focus of the modern biomedical applications. This technology relies on strong interactions of dynamic and magnetic degrees of freedom of the system. Here we study in detail various experimentally observed regimes of the helical nanomotor orientation and propulsion depending on the actuation frequency, and establish the relation of these two properties to the remanent magnetization and geometry of the helical nanomotors. The theoretical predictions for the transition between the regimes and nanomotor orientation and propulsion speed are in excellent agreement with available experimental data. The proposed theory offers a few simple guidelines towards the optimal design of the magnetic nanomotors.