"A place in the commonwealth" describes Brutus's ideal vision for the Roman state. He wants Rome to remain a republic, where no one individual has too much power over the Senate and the masses. He believes everyone will benefit from Caesar's death, even Mark Antony, who was one of his staunchest supporters. Brutus shows how little self-interest he had in the murder by claiming he would kill himself for the common good, too, if it was deemed necessary.
This whole section is to show how idealistic and noble Brutus is. He is not ambitious, and he loved Caesar, unlike the other conspirators, particularly the jealous Cassius. He had every reason to not go through with the stabbing, but he put aside his own desires for the common welfare. He includes Antony in this vision, not just because he believes it to be so, but also to help sway Antony to his perspective. He wants to pacify everyone as soon as possible.
Unfortunately, this does not work once Antony takes the stand and explains Caesar's plans for helping the Roman people. Then, Brutus appears foolish and ignorant, and the people turn on the conspirators.