Your first step in researching this might be reading the beginning of the play. Hamlet is initially set on his course when the ghost of his father appears and demands that Hamlet kill Claudius, because Claudius had killed Hamlet's father and married Hamlet's mother.
Hamlet and his friends are initially skeptical about the ghost, worried that it is demonic or evil. Thus Hamlet is extremely hesitant about committing murder and refuses to do so until he has firm and incontrovertible truth that Claudius is indeed guilty. The death of Polonius is an accident.
Hamlet is given firm evidence of Claudius' intentions first by reading the instructions Rosencrantz and Guildenstern are given to kill him and then by Claudius' reaction to the play. Gertrude's death is due to drinking poison Claudius intended for Hamlet.
Given that the character of Hamlet is distinguished by reluctance to act and a need to be assured that any action he takes is justified, the play quite clearly assigns revenge as his motive.