It’s probably easier to try and pick the best, given that so many emperors were incompetent or completely insane. Caligula, the incestuous sister-murdering, foetus-eating lunatic, for example, or Commodus, who also an incestuous sister-murderer (although he never ate his own unborn child).
I’m just thinking of Western emperors, so excellent chaps such as Basil II and John Comnenus don’t come into it. There are a few contenders, including the long-reigning Augustus and Constantine, the wise and subtle Diocletian and the conquerors Trajan and Aurelian.
I would not even consider Marcus Aurelius. Yes, he was a philosopher and kind and sensible, but he also made an absolutely appalling error of judgement which was critical in the long term destruction of Rome. Previously, Nerva, Trajan and Hadrian had nominated others as emperors rather than letting it be hereditary. This worked tremendously well, as each emperor wisely picked a top chap (or chaps, as Hadrian picked two Antonines, the younger of which was Aurelius). But Marcus Aurelius then, stupidly, not only broke with tradition but did so when his own son proved to be an appallingly awful emperor. Commodus ruled for over a decade, murdering numerous excellent senators, playing as a gladiator and generally terrifying the upper classes until his own household pre-emptively killed him before he could slay them.
After this, the Praetorian Guard effectively become the rulers of Rome, installing or destroying emperors and the habit of regicide became firmly ingrained in the Roman system. And all because the philosopher broke with tradition.
I’d consider Constantine a contender, but not the very best. Undoubtedly he had many virtues and enjoyed great victories, particularly in the early part of his reign. It is debatable whether his selection of Byzantium as a new capital removed any hope of Rome’s own survival as a real power or whether it enabled the Eastern Empire to thrive when it would have collapsed otherwise. But, he became a tyrant later in life, murdering his own excellent son, Crispus, and his wife.
Trajan enjoyed almost unfettered success. Under him Rome’s empire grew to its largest ever size (briefly, the territory of modern day Iraq he conquered was soon left for the Parthians to retake) and he also established the new province of Dacia. The only potential reason not to consider him the greatest of emperors is that he reigned during the time of Rome’s zenith, so it was a bit like being manager of a Brazilian football team that wins the World Cup.
Two of my favourites, recently read about in Edward Gibbons’ Decline and Fall of the Roman Empire, were the Gothic Claudius (not to be confused with the successor of Caligula and forerunner of Nero) and Aurelian, who ruled during the time when Rome’s power was rapidly waning. Claudius smashed the Goths in battle, but died after a short time as emperor, succumbing to smallpox.
Between the reigns of Claudius and Aurelian was that of Quintillus, which lasted less than a year. Aurelian was emperor for about five years, during which time the empire was rife with insurrection and self-declared emperors. Following in Claudius’ footsteps, he bested the lot of them, including the interesting Zenobia, an empress of Palmyra. In fact, he was so successful he got the (pretty deserved) title of Restorer of the World. [I plan to get a history of him in the nearish future].
However, even the tremendous success of Aurelian could not prevent the regicidal habit, and the Romans, at this stage annoyed by his strict regime, killed him. Aurelian’s conquests extended the Western empire by centuries, but his death prevented any prospect of returning to the Nerva-Antonine golden age.
Diocletian was a more practical sort than Marcus Aurelius, but he also made a similarly enormous error. He established the tetrarchy, ruled by two senior Augusti (with himself as top dog) and two junior Caesars. Whilst he was in charge it worked well, but when he abdicated the system, predictably, led to fragmentation and yet more civil war. At one point there were six emperors, from which Constantine alone emerged victorious. It’s also worth mentioning that Diocletian oversaw widespread persecution of Christians, but they had the last laugh when Constantine converted.
Of the above, I’d pick Aurelian as the best. He enjoyed constant success despite facing numerous opponents and his successes bore strategic fruit. A little more moderation in civil administration might have seen him live longer, but his victories saved Rome and came at a time when the empire could have fallen or fragmented.