The person considered the first Emperor of the Roman Empire was Augustus Caesar. He reigned from 27 B.C. to 14 A.D. and was one of the very few Roman rulers who died on natural causes. After his rule came Emperor Tiberius (14 to 37 A.D.), Caligula (37 to 41 A.D.), Claudius (41 A.D. to 54 A.D.), and Nero (54 to 68 A.D.). Nero is the first Roman ruler to carry out a state-sponsored persecution of Christians.
After Nero's death, the empire entered a period of civil war known as the 'Year of Four Emperors.' In this period, four emperors would rule in quick succession. Galba reigned after Nero until his murder in June 68 A.D. Otho then ruled until he committed suicide in April 69. Vitellius then rose to power and ruled until he also was murdered. After his murder, the Senate declared Vespasian sole ruler of the empire on December 20th of the same year.
Vespasian ruled for about ten years until his death in 79 A.D. Titus succeeded him, but only was Emperor for two years until the plague took his life. Domitian, who began Rome's second persecution against believers and who banished the apostle John to the isle of Patmos, reigned from 81 to 96. He was followed by Nerva (96 to 98) then the last first century emperor Trajan (98 to 117 A.D.). It was Trajan who conducted Rome's third state persecution of those who believed in Christ. He is also historically known for reigning the Empire during its height of power.
There are four emperors mentioned or specifically referred to in the New Testament. They are Augustus (Luke 2:1), Tiberius (Luke 3:1 - His death might have been by assassination), Claudius (Acts 18:2 - who was likely poisoned in 54 A.D.) and Nero (who is referenced in Philippians 4:22). It is under Nero that both the apostles Paul and Peter lost their lives.