First of all, the "bonfire" rockets are millions and millions of times lighter than a real NASA rocket! So, it takes very little energy to get them moving.
A real rocket is incredibly massive, and if I'm not mistaken there are balancing systems aboard the ship that tell the engines to fire more/less to help keep the rocket going in the right direction.
It takes an amazing amount of energy to get a large craft like that moving, and there's only so much fuel you can place into a rocket and still get it off the ground. It does move faster the higher the rocket goes because the earth's gravitational force decreases with height AND the mass of the fuel gets used up making the whole ship lighter.