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.