I would give it to
Aurelian for restoring the empire as first.
Second is
Augustus
Augustus model probably resulted in less civil wars than if he wasn't there, but I see it as a mark against the man that he spent so much time killing other romans. His legacy was lucky in that his ambition and power hunger combine with the fact that the roman empire was so big that it would bring forth civil wars by power hungry generals. By winning the prize and establishing it, he probably saved it from more carnage than if he lost and there were civil wars until another Octavian like figure (successful charismatic dictator) came out. But who knows what form that would take. Also, his success had something to do with those and Julius Ceasar civil wars, and even a bit the previous civil wars of Marius and Sulla. To make it short, the Romans were sick of that shit. That probably gave the empire some good will.
Very important is that he expanded the empire in almost all directions and helped stabilize past and current conquests. Unfortunately he failed to successfully expand as much as he wanted with Germania, in part due to the illyrian revolt and his successors didn't follow suit. Obviously his cooperation with the great Agrippa helps elevates him.
He loses a bit due to operating when the roman empire was relatively uncontested and trouble with successors.
He gains a bit for extensive building program.
Followed by Hadrian as third who did allright but where he becomes third is because he chose as his successors Antoninus Pius and Marcus Aurelius. That is a stretch of 67 years of good emperors doing a good job. Which is actually really impressive when you consider the quality of many of the emperors who ruled. Both Hadrian, and Pius and Aurelius create this image of a philosopher king, which I appreciate, and they were likely aware of the concept.
As for his own leadership, again he elevated military discipline, and while he ruled competently, I tend to agree with the view someone else expressed that there should been abadonment of Britain and greater focus on retaining more influence in the east. Without choosing good successors he wouldn't be third but still likely somewhere in the lower parts of top ten. Still he is very unique in managing to enlist not one but two other emperors that are in the top ten.
Very Closely followed by Fourth is Costantine with his choice of Constantinople having a hugely influential role. He reminds me of Augustus in that he broke up a system that were poised to be about civil wars, was ambitious and power hungry, was hugely influential, and his successor wasn't all that great. He also did very well as a military commander. Where he loses is in that he decided to seperate the empire to his kids which is an incredibly monomumentally stupid idea, with an inevitable conclusion.
It looked like this:
https://en.wikipedia.org/wiki/Const...e:Impero_Romano_da_maggio_a_settembre_337.png
I might be underrating Constantine a bit, he does remind me a lot of Augustus. He also didn't need someone like Agrippa.
The same position of fourth is for Trajan who did such a good job, he was known as the epitome of leadership.
Really, you could arrange the positions of people in 2-4, with perhaps Hadrian not being as monumentally important as the others but being unique in choosing two good successors. Only Aurelian to me is clear number one.
Fifth is Galerius who accomplished the most decisive victory against the Persians and sacked their capital.
Sixth is Carus, who ruled only for a year but managed to inflict good defeats to the Persian and again reached even further from their capital after after successive roman emperors were mired by defeat against the Persians and Shapur. Now, the Persians did have civil trouble, but he took the opportunity. He ruled for only a year because he died by illness at camp which was unfortunate for the Romans as they could have pushed further. Maybe his name would be as legendary as Trajan if he didnt die (by either illness, bolt of lightening or poisoning) and he continued that campaign.
Other interesting aspects, he also seperated the empire between his sons, arrangements of power sharing are actually not that uncommon among the romans, where it became especially dangerous for the roman empire is where they sticked, especially with Theodosious progeny, or where they lead to civil wars between east and west. (Ofcourse there was also Valens and Valentian previously). Anyway, despite frequent cases of someone focusing on one side, another on the other, it didn't tend to stick.
Seventh is Vespasian who gains points for not only being a good emperor but for having talented kids who did a good job as emperor. And really, I see the legacy of a succession of one good king and then another to be something you see from Vespasian's time, instead of the (other) Flavians.
Between his dynasty, Trajan, Hadrian and friends, and Augustus time, you have most of the period of good leadership for the roman empire before the crisis of the third century. You have eight good emperors.
I am unfair towards Marcus Aurelius and Antoninus Pious but because I mentioned them in Hadrian's case, I am not sure exactly where to place them, so lets place them here.
Eighth is Marcus Aurelius. He ruled with competence, and faced rising military threats with success. Might not be fair to blame him for that, but unfortunately his son was one of the worse emperors. I am not blaming him for it, but I do see with more positive when emperors chose good successors or raise their kids to be competent people.
Ninth and ten is Gallienus and Antoninus Pius
Ninth is Antoninus Pius who not only ruled long with peace but chose to honor Hadrian's chosen successor and chose Marcus Aurelius.
Ten is Gallienus ruled during a challenging time, Aurelian build uppon Gallienius reforms, including a focus on large cavalry units to be dispatched swiftly in different parts of the empire. He did rather well at fighting back agaisnt barbarians but couldn't hold back many revolts. I am not sure most of the fault should go to him for that though, but maybe a little might have to do with himself. Still he ruled when shit really hit the fan, and helped to overcome that.
So that is the top ten, and they were all good emperors that contributed to the empire's success and longevity and lets add one more place.
11th is Diocletian. I see his economic reforms are mostly bad, but most roman emperors didn't do a particularly good job. He was successful militarilly and helped Gallerus campaign, ruled for long, and appointed some competent rulers and Constantine. That is enough to get him at 11th. If Constantine didn't stop the tetrarchy I wonder if it could have proved to be a big detrimental disaster. During Diocletian's time it worked somewhat to a point, towards external enemies but even during his own lifetime it proved unstable.
In the same position, let's add the regent
Anthemius, who really rulled when Theodosian II was a child. He commanded building the Theodosian walls that were so important for the eastern roman empire and though this is a bit of cheating, his capable leadership deserves a mention. Also it is the number 11, so I can play around a bit with my selection. It is also tragic that he disappeared and theodosian's less capable sister became regent. It needs to be said that during this period, the eastern and western empires were in the transformation if not already done of being different politeies (but both were romans), this was detrimental to both, but more to the western empire which was weaker. A bit of cheating here but he deserves to be known more.
So the names I mentioned are most roman emperors who come to mind at doing a good job for these time periods. If we extend to the later periods (known as the Byzantine ones) there are others.