How I see it is this way; 

All the liberators/conspirators, excluding Brutus, were jealous of Caesar's power. Maybe  not jealous, but they didn't want to be ruled by him, or any 'king'. Almost all senators, even the ones who didn't know about the conspiracy, didn't want to be ruled under one man, let alone, arrogant Caesar.

Don't get me wrong, Caesar is nothing of a tyrant compared to the monster he created (Octavian.) I'm talking historically, not in the play. So is Antony, all the cared about was revenge, money and control over Rome. Octavian then turned against Antony, who was ruling over their east part (including egypt) with his beloved Cleopatra. 

Before that, Antony and Octavian started killing Senators, why? 

1- Money

2- To make people fear them.

3- Simply because they don't like them.

They also killed commoners so they won't have to give them Caesar's money will. They were greedy heartless monsters, weren't they?