Actually, both gravity and inertia must be overcome. Gravity to get the spacecraft into space, and inertia to keep it there by moving it horizontally so fast that the earth falls away before the spacecraft can fall back onto it.
Ignoring thrust, air drag and other perturbations, the sum of a satellite's kinetic and potential (gravitational) energy remains constant. In a circular orbit they are also individually constant, but in an elliptical orbit some of the energy moves back and forth between the two forms.
In a low earth orbit nearly all of the total (~95%) is in kinetic energy.
KE + PE = constant is true even for an open, hyperbolic 'escape' trajectory like that of the Pioneers, Voyagers and New Horizons as they leave the solar system. As they gain potential energy climbing out of the sun's gravity well, they slow down to lose an equal amount of kinetic energy.