First Option: It Decreases.
Gravity effect an object that has more mass, and/or is closer. So as the Spacecraft leaves Earth, Earth's gravity becomes less relevant. To fully understand this think of Eisenstein Theory of relativity as it relates to gravity. Though still a Theory, I know, just go along with it because it will help you understand.
Think of the fabric of space and time. Literally, a fabric, such as a blanket. And if you put a basket ball in the middle it will form a dimple in the blanket. Then take a bouncy ball. the closer the bouncy ball is to the basket ball, the faster it is pulled in. You will find the same thing with a bigger ball.
The bouncy ball is what I am talking about when I say the closer you are the stronger it is. As you have mentally simulated, the closer you are to the basket ball, the steeper the dimple, which means the faster it is pulled in. Same with how a bigger ball goes to the center easier than a smaller ball at the same distance.
The planets don't all crash into the sun because if you hold a glass half filled with water, extend your arm out with the glass in hand, you will find that the water in the glass goes the outside of the circle you are spinning. It is pulling away from you. In this manner satellites, space stations, moons, etc. can orbit each other. There is and equal pull outward from the spinning as there is with the gravitation force seen on the blanket.
