The central question you have to ask yourself about the character of Marc Anthony is if he is a political opportunist, motivated to rise against the conspirators to seize power for his own selfish ends, or is he genuinely a great admirer of Caesar and forced to act to prevent the conspirators seizing power.
Interestingly, the character of Marc Antony is a minor one at the beginning of Julius Caesar, but he rises in prominence, especially in Act III. Other characters regard him as a bit of a "lad" or a playboy, and his habit for keeping wild company and partying is something that prevents other characters from taking him seriously. His first appearance in the play is in the games in honour of Lupercal, and Caesar states that Antony "revels long o'nights."
Antony is led away from the assassination and after the deed has been committed he asks to meet with the murderers. There, he laments the death of Caesar and praises him. Brutus and the other conspirators are unsure of his motives, but Antony assures them that they have acted in wisdom before praising Caesar again. Antony is allowed to address the crowds at Caesar's funeral.
It is after the conspirators leave that Antony delivers his first soliloquy of the play, where he states his intention to have his revenge on the conspirators. Because this is a soliloquy, critics have argued that this shows he was motivated by grief and love of Caesar rather than any power-mongering intention, but this is one of the questions you will need to ask yourself about Antony's motivations. It is during his oration that Antony clearly manipulates the crowd and stirs them into a frenzy against the killers of Caesar. He displays his impressive rhetoric skill and wins his objective of turning the mob against the conspirators.
The last Act further confuses the picture we have of Antony. At one stage he coldly agrees to the death of his nephew in exchange for the death of the brother of Lepidus, but then, when Brutus is captured, ensures that he is taken care of and states that Brutus, alone of the conspirators, acted for what he believed to be the general good. Thus the question has to be asked about whether Antony is self-serving and a political opportunist, or whether he is a genuinely good man, provoked into taking power by the assassination of Caesar, a man he loved and admired.