How much did the events under Marius and Sulla impact Caesar, Pompey, and Cicero’s generation?
Julius Caesar witnessed the takeovers and tyrannies of Gaius Marius and Lucius Cornelius Sulla at the very impressionable age of his early teen years; hence, it can certainly be argued that Marius's and Sulla's actions significantly influenced Caesar's own future political maneuvers.
In 88 BC, political conflict between Marius and Sulla developed into a civil war. The conflict arose when King Mithridates, king of Pontus, attacked Roman-held territory in Asia, resulting in the deaths of 80,000 Romans and Italians. Yet the Roman Republic felt conflicted over who to send to defend Rome. The senate wanted to send Sulla, while the Tribune of the People Suplicus Rufus nominated Marius (Illustrated History of the Roman Empire, "Gaius Marius"). In response, Sulla marched against Rome, putting to death all of Marius's supporters, leaving Sulla to be the man to defend Rome against Mithridates (United Nations of Roma Victrix, "Julius Caesar: His Early Years"). But while Sulla was away, Marius and Lucius Cornelius Cinna retook Rome in another "bloodbath" ("Julius Caesar"). Marius died of natural causes, though, soon after his victory, leaving the door open for Sulla to regain command. Under Sulla's reign, Caesar's life was threatened because Caesar was nephew to Marius. Caesar went into exile, but Caesar's family was able to persuade Sulla to spare Caesar's life.
In 81 BC, Caesar enlisted in the Roman Army, which led him on a number of successful campaigns (History Learning Site, "Julius Caesar"). His military successes guaranteed the loyalty of his 50,000 troops. Meanwhile, he also made enemies, including senior general Pompey. Under Pompey, in 49 BC, the Senate commanded Caesar to relinquish control of his army and Caesar refused, which was considered treason. Regardless, one year later, Caesar fought against Pompey, killing him in Egypt. Over the course of the "next three years [Caesar] picked off his enemies one by one whether they were in North Africa, the Middle East or Europe" and returned to Rome in 45 BC to rule as dictator (History Learning Site).
We can certainly see Caesar's violent responses to political issues as having been influenced by the violence of Marius and Sulla.