Which character in Julius Caesar searched for and arrived at a sense of identity?Please explain what led this particular character to arrive at...

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.