While Brutus, Cassius, and Marc Antony all possess certain foibles, Antony is the most consistent in character. From the beginning of the play, he demonstrates great loyalty for Caesar, walking beside him as he enters the city, grieving privately for his fallen leader, and aligning himself with Caesar's nephew in his efforts at vengeance against the conspirators.
That Antony's feelings for Caesar are genuine is established, critics agree, because he grieves privately for the fallen leader:
O pardon me, thou bleeding iece of earth,/That I am meek and gentle with these butchers!/Thou art the ruins of the noblest man/That ever lived by the tide of times,/Woe to the hand that shed this costly blood! (III,i,254-258)
Immediately, too, he sends for Octavius Caesar and does not consider any avenue for himself to gain in power. Still loyal to Caesar and steadfast in his determination to discredit Brutus and the others, he composes a funeral oration that incites the Romans to turn against Brutus and the other conspirators.
While Cassius is envious of Caesar and Brutus too idealistic and easily swayed by the seduction of the words of Cassius to enlist him in the conspiracy against Caesar, Marc Antony's plans remain true to avenging the death of Caesar. Although he does display callousness in the proscription scene of Act IV, he does maintain his purpose in pursuing Brutus and the others, unlike Brutus who becomes guilt-ridden, seeing the ghost of Caesar and Cassius, who becomes superstitious and weak, acquiescing to Brutus's poor battle plans and worrying that Brutus no longer loves him. Not possessing the "thick" sight of Cassius either, or the poor judgment of Brutus who is defeated at Phillippi as a result, Marc Antony retains the vision to see the nobility in others: When Lucilius is taken prisoner, he instructs the soldiers to treat him well. And, when Brutus dies, Marc Antony honors Brutus as "the noblest Roman of all." (V,v,68). Indeed, from the beginning of Shakespeare's "Julius Caesar," until the end, Marc Antony possesses a strong sense of self and purpose.
While you could argue for some other characters, Brutus and Antony best answer the first part of your question. When Cassius comes to Brutus with his plot to get rid of Caesar, Brutus does not at first agree; he takes time to mull over Cassius comments about Caesar's ambition and to rethink the crown situation (Caesar's refusing the crown three times). Even Cassius's "anonymous" notes which encourage Brutus to help Rome by eliminating Caesar do not convince Brutus. Instead, he comes to his own decision about what needs to be done, and once he does, he runs the assasination plot. When he gives his funeral speech, many believe that he was sincere about killing Caesar for Rome's good; the speech is Brutus's one opportunity to try to establish who he really is with the people. At the end of the play, Brutus does realize that while he had noble motives for killing Caesar, he actually made the situation in Rome worse (in regards to power-hungry leaders). This is his sense of identity--he most likely knows how he will go down in history.
Antony has a more positive experience with his recognition of self. Before the conspiracy plot, many viewed Antony as simply an unthinking gopher, ready to do Caesar's bidding. However, when he delivers his masterful funeral speech and sways the crowd to turn against the conspirators, it is obvious that Antony realizes what his words have the power to do. From that moment on in the play, he reveals himself to be unflinching and shrewd in his takeover of the republic.