Darius and Xerxes were Persian emperors who were more concerned with destroying Greek culture and influence than spreading it. Julius Caesar was a Roman General and then later, briefly, an emperor. Leonidas is the man immortalized in the story of the battle of Thermopylae who lead a small force of Spartan soldiers against the seemingly endless might of the Persian Empire. Of the provided answer choices, only Alexander the Great was both Greek and a conqueror. Alexander the Great lead Greek and Macedonian forces on a massive campaign across North Africa, the Middle East, and Asia that did not end until he reached Northern India. He is often partly credited with the overwhelming influence that Greek culture has had on the world’s languages, cultures, religions, philosophies, and politics. 

Of these famous ancient Greek individuals, only Sophocles is famous for his dramatic, specifically tragic, plays. Socrates and Aristotle are both famous for their philosophical and scientific writings and teachings (Socrates taught Plato, who taught Aristotle, who taught Alexander the Great). Pericles was the most famous political figure in Republican Athens. Finally, Thucydides is remembered for his historical writings, particularly his History of the Peloponnesian War, a chronicling of a war that was fought between Athens and Sparta in the fifth Century BCE.

The First Triumvirate of the Roman Empire was formed between Julius Caesar, Pompey Magnus, and Marcus Crassus. The Triumvirate had no legal authority and was formed solely to consolidate the power of these three men against the legal authority of the Roman Senate. Following Crassus' death, a civil war erupted betwen Pompey and Caesar that ended with Pompey's defeat and Caesar assuming the role of dictator of Rome until his assassination ten years later. 

Draco and Solon are somewhat enigmatic figures in Ancient Athenian history. They were both lawmakers. Draco came first and extended democratic rights to those Ancient Greeks who were wealthy enough to afford armor (not the arbitrary distinction this might seem now, as these were the men who fought for/funded the defense of Athens). However, his laws were extremely harsh - prescribing punishment by death for just about every crime. It is from his name that we get the English word “draconian.” Draco’s legal system did little except pit the poor against the rich in Ancient Greece and so the Athenians turned to Solon to revise the political system in Athens. Although neither Draco nor Solon themselves created the institution of democracy in Athens, their legal codes and political reforms were the foundations upon which the original Athenian democratic society was able to grow. 

Thucydides is probably the most famous classical era historian. He is most famous for his writings on the Peloponnesian War between Athens and Sparta in the fifth century B.C.E. 

Euripides, Sophocles, and Aeschylus are the three Greek tragedians whose work has survived. Sophocles is probably the most famous of the three, although this is somewhat subjective, and he gave us the story of Oedipus. 

Hippocrates is often considered to be the "Founder of Western Medicine." Among other things, Hippocrates is credited with advancing physiological and anatomical understanding. He also proposed the Hippocratic Oath which continues to influence doctors to this day. 

The First Triumvirate of Rome was a political alliance between Julius Caesar, Marcus Crassus, and Pompeius Magnus. It was not an official political organization, but rather a secretive organization that sought to engineer the downfall of the Roman Republic. Following Crassus’ death the Roman world was essentially in the hands of two men - Pompey (his anglicized name), who controlled the Senate and Julius Caesar who controlled the armies of Gaul and enjoyed the most popular support. When Caesar crossed the Rubicon he was declared an enemy of the state and Pompey was charged by the Roman Senate with defeating him. Thus ended the First Triumvirate of Rome; when Caesar defeated Pompey in battle and then had him assassinated. 

The Roman Emperor held a number of different titles, including pontifex maximus, which is Latin for "chief priest". The title was held by Julius Caesar as a pre-Empire designation, but given to his adopted son Octavian. When Octavian became the first true Roman Emperor with the title Augustus, he kept the designation of pontifex maximus, which was passed on to later emperors.

As Christianity developed during the first century CE, its earliest followers  were persecuted in the Roman Empire. Not until the Edict of Milan in 313 CE was Christianity even legal in the empire. Therefore "the widespread acceptance of Christianity" is the correct answer.

All of the other answer choices were true of Rome during the first century CE as it approached its height in the early second century CE.