Discuss which character is the most Machiavellian in seeking what is best for Rome in Julius Caesar.
You might want to review your appraisal of The Prince (Machiavelli's treatise on the ruler and the best ways for him to maintain power) in considering your question. The most "Machiavellian" character in Julius Caesar will probably not be acting in consideration of "what is best for Rome," since, in following Machiavelli's precepts, he would be looking out for his own interests in maintaining public support to hold his position of power, of rulership.
I would suggest that the character in this play who does the most to maintain his position and the support of others -- whether it be of the public, of the current ruler (Caesar), or of those who attempt to usurp power (the Conspirators) -- is Antony.
In Act I, Antony is portrayed as a right-hand man to Caesar, and has acquired a position of much power in this popular positioning of himself. In Acts II and III, he manages to keep on the good side of Brutus (up to the chaotic ending of the funeral orations), which means that he retains the support of the Conspirators, even though some believed that he should die alongside Caesar. And of course, he wins the unequivocal support of the masses when he delivers his emotionally stirring funeral oration over Caesar's dead body.
But Antony really shows his Machiavellian ability to behave as the moment dictates in order to preserve his power in Act IV. He is cold and calculating with Lepdius and Octavius, plotting with Octavius behind Lepidus' back, while also planning the deaths of the Roman Senators who do not support his position.
The end justifies the means for Antony. He takes on whatever position will preserve his position of power, even if it involves a bit of role playing (as he demonstrates when he manipulates Brutus into allowing him to speak at Caesar's funeral). In the end, Antony (along with Octavius) gains the supreme position of power in Rome, and he employs the Machiavellian strategy of "looking out for number one" in order to gain it.
For more on Antony and on The Prince, please follow the links below.