In order to write a first-person narration from the perspective of Julius Caesar, one must understand his perspective of certain events and take into account his view of himself throughout the play. Caesar is a vain leader, who is extremely self-confident and dedicated to maintaining his position. Initially, one must comment on Caesar's dismissal of the warning given by the soothsayer. Caesar calls him a "dreamer" and dismisses the premonition in act one. Caesar's self-assurance does not allow him to take the soothsayer seriously. Caesar then reveals his suspicion toward Cassius by commenting to Antony that he does not trust Cassius in act one, scene two. If one were to elaborate on Caesar's thoughts, they would include his desire to maintain power at all costs. One might also want to include Caesar's thoughts concerning how the Roman crowd cheered as he pushed away the crown Antony presented to him three times. According to Casca's interpretation, Caesar was reluctant to refuse the crown.
In act two, scene two, Caesar seems perturbed by Calpurnia's dream, but his self-confidence does not allow him to fear the foreboding omen. He also refuses to be viewed as weak and insists on attending the Senate after hearing Decius's interpretation of Calpurnia's dream. Caesar's arrogance could be depicted when writing about the events that took place in act two.
In act three, Caesar is warned again but refuses to read Artemidorus's letter. Caesar thinks the man is insane and does not want to tarnish his public image by giving credence to such a man. In front of the Senate, Caesar dismisses Metellus's request to pardon Cimber and elaborates on why he will not pardon him. Caesar then begins speaking in the third-person as he once again displays his vain nature. One might comment on Caesar's elevated view of himself as a just leader during this scene. As the Senators attack Caesar, his last words are "Et tu, Brute?" (Shakespeare, 3.1.85). One could elaborate on Caesar's feelings toward the treachery expressed by such a close friend as Brutus.
This is a great assignment. In order to do a good job, you will need to know the story well, and more importantly know Caesar's personality well, so that you will be able to speak from his perspective and his voice.
As for events leading to Caesar's assassination, there are a few important points to bear in mind. First, you should add the supernatural events that Caesar ignores. Caesar ignores all the signs of the gods - the soothsayer, his wife's dreams, the storm, and other prodigies that show that all is not well. To put things into the Roman context, these are all signs of ira deorum.
Second, the people really do favor Caesar. They shout his praises on the streets. Therefore, the conspirators are afraid that his popularity will enable him to be king. There is real fear.
Third, we have Caesar's stubbornness. As Caesar says "he is as constant as the Northstar." In other words, nothing can deter him from anything, such as going to the courthouse on the ides of March.
Based on these points, you should be able to write a first person narrative. I would characterize Caesar as noble, stubborn, brave, generous, and constant. In light of these point, I would also make him blind to the jealousy of others, which could be part of his tragic fault.