Gravity is a constant force pulling objects towards the earth's surface, for a rocket to even get off the ground it must create more thrust than the rocket's mass. The only thing that can be done to combat gravity is to make rockets as light as possible (while still being strong)
Drag is a force experienced when any body moves through a viscous medium, although air does not create much drag at low air speeds the force becomes considerable over speeds at which rockets travels at, hence the slender and very aerodynamic shape of a
Thrust is the force which propels the rocket into the air. By virtue of Newton's third law states "for every action there is an equal and opposite reaction". The action in this case would be the thrust and the reaction would be increase in airspeed and increase in drag. If the rocket creates more thrust than its mass and the drag affecting it, then the rocket will accelerate in the direction of the resultant force. If the rocket creates more thrust than its mass, but the it's mass and drag force are equal and opposite to the direction of the thrust, then the rocket will move with constant velocity. The thrust is created by a motor (a device which imparts energy).Click here for more info.