The best way to learn about the Roman republic is to start with the works of Michael Grant. His writing is enjoyable and not overdown like that of some historians.
My favorite is The History of Rome. Charles Scribner's Sons, New York, 1978.
Grant has also written, The Gladiators, Julius Caesar, Nero, Fall of the Roman Empire, and others.
For more detailed look at the history, consider the work of H.H. Scullard. A History of the Roman World 753 to 146 B.C, Routledge Press, London & New York, 1980. His also wrote a companion work titled, A History of the Roman World 133 B.C. to 68 A.D.