The purpose of the ghost beckoning was his way of showing that he wanted to talk with Hamlet alone. He wouldn't talk to anyone but Hamlet.
"Born to set it right"
The talk between Hamlet and the Ghost is what initiates Hamlets indecision.
"Now I am alone"
O, what a rouge and peasant slave am I!
Right after the ghost parts, all Hamlet can think about is how he vows revenge on his mother even though the ghost said to leave her alone.
"I'll catch the conscience of the King"
Hamlet is very puzzled . He isn't sure what to think, but all he knows is that he has many forms of revenge on his mind that he wants to accomplish.
Hamlets internal indecision leads to him getting very frustrated with himself that he can't figure out what to do. Hamlet wishes he could act and not lack the guts to do things.
After a lot of thought Hamlet finally comes to the conclusion that he will have the Players put on a play about revenge and death to see if he can get a reaction out of Claudius. His indecisiveness is very apparent as he wants evidence of Claudius's guilt.