Final answer:
Stoicism, a Hellenistic philosophy, was the most favored by the Romans during the Republic, due to its emphasis on virtues like self-sacrifice and rationality, which resonated with Roman ideals.
Step-by-step explanation:
The Hellenistic philosophy that most appealed to the Romans during the Republic was Stoicism. Emphasizing self-sacrifice, strength, political service, and the rejection of frivolous luxuries, Stoicism aligned closely with Roman values. By the first century BCE, many aristocratic Romans had embraced Stoicism, with its focus on living in accordance with nature and the universe, which was believed to be governed by divine reason or Logos. This alignment with Roman virtues of discipline and duty, valuing wisdom and moral virtue over material excess, made Stoicism the philosophy of choice among Roman leaders and intellectuals.
Among the different schools of Hellenistic philosophy, such as the Epicureans and Cynics, Stoics stood out for advocating that true happiness came from accepting fate and cultivating internal virtue. Despite external circumstances, a Stoic sought tranquility through living in harmony with the natural order. Famous Roman Stoics, including the emperor Marcus Aurelius, further cemented Stoicism's influence in Roman culture, emphasizing its practices as a guiding framework for Roman leadership and ethical conduct.