In Shakespeare's Julius Caesar, so much of what is pertinent to the play comes from Brutus and Antony: they are much different men and motivated for totally different reasons. Brutus wants the best for Rome; Antony wants Rome. These two characters are also essential in that...
Antony's and Brutus's use of rhetoric, or persuasive language, has a decided effect on the dramatic action in Julius Caesar.
If I were in your situation, I would do a number of things. I would make sure I know who each character is in Acts Three and Four. Whether they are newly introduced or have been in the play since the start, I would review each so that when I read on, I will know how each character fits in.
I would make sure I am overly familiar with the action in these two acts. Reading the eNotes' summaries, and each summary with the corresponding analysis for each act would be essential. I would probably read these at least twice.
It would be important to pay attention to any stage direction throughout the two acts: these directions often offer added insight as to what the characters on the stage are doing.
It is important to note that if you are not studying the speeches of Antony and Brutus verbatim, make sure you know at least what they characters are saying—have an understanding of the essence of the speeches. I would read the eNotes' translations for the speeches so that you can understand the action surrounding them. Without the speeches as a referent point, I believe much of the continuity of the plot and the subsequent comprehension would suffer.
In Acts Three and Four, there are several central plot developments that deserve extra attention. One is...
As he begins the day’s proceedings, Caesar’s ego is apparent.
This is relevant to Brutus' perception that Caesar cares more for self than his people or the Roman Empire. This will motivate him to act as he sees fit; and this example does not come from speeches by Antony and Brutus.
Another central plot development is...
...the question of whether Caesar's assassination should be considered murder or a justifiable action.
This affects how we see Brutus, primarily: if he is justified in killing Caesar, we see him differently than if he was simply a murderer. (This question of whether it was ever justifiable to kill a king—regicide—concerned the Elizabethan audiences, not just "Brutus" or Shakespeare.)
With this said, in studying the surrounding material in the play, read the translations before and after the speeches, perhaps before you begin to study/review, and after.
You will also want to pay particular attention to the characters of Brutus and Caesar in order to best understand the actions of each and the outcomes in the play. Important information lies in...
...the private and public values of Brutus and Caesar and the relationship between human endeavors and history.
If you know the key elements of these two acts, and understand the content of Brutus and Antony's speeches, you should be in good shape to make sense of the behaviors and dialogue of other characters in sections of the play surrounding the speeches in Acts Three and Four..