I teach history at a community college. I do both online and face-to-face classrooms. I was just thinking about next week's assignments and how exactly I will answer this question.
One of my words is certainly "tradition." There is such an interesting feedback loop into what Americans look back to as "tradition" from the Romans, and what the Romans themselves looked back to as tradition. Mos maiorum meaning "the way of the ancestors"... is just a little insight.
Romans continued to call themselves a republic after they were arguably a dictatorship, in part because of tradition, no?
Second word, "influential." Sometimes I ask whether Byzantine or later was a continuation of Roman culture, or something new entirely. Not new ideas, I know. In either case, both answers insist that the Romans were incredibly influential.
Virtus
Disciplina
These two words sum up, in my opinion, the Roman people and their history at an internal level. I do like your explanation of Tradition and Influential as we look at the internal/external mechanic of the Roman empire and the impact it had on the world around it and even in our world today. However, looking just internally, I like like these two Latin words for reasons I'll lay out.
• Virtus
This word can mean manliness, manhood, goodness, virtue, excellence, worth, resolution, valor, or various other words that extend a meaning of courage and martial skill. Adrian Goldsworthy in his biography on Julius Caesar and his book "In the Name of Rome" goes into some detail on the ideals of virtus in the Roman martial consciousness. It was a defining trait in the founding of Rome and a required trait in the greatest men and leaders of the Republic and the Empire.
It is talked about in Plautus' work, when a wife sings:
I want my man to be cried as a victory in war: that's enough for me. Virtus is the greatest prize, virtue comes beforee everything, that's for sure: liberty, safety, life, property and parents, homeland and children it guards and keeps safe. Virtus has everything in it: who has virtue has everything good.
This spirit of martial courage and personal bravery was a key component in winning Rome the empire.
• Disciplina
This word means instruction, knowledge, discipline, system, method. It speaks to the balance between martial courage of virtus and the necessity of keeping the bigger picture in mind. This is talked about extensively in JE Lendon's book "Soldiers and Ghosts: A History of Battle in Classical Antiquity"
This concept of disciplina is the flip side of the Roman martial spirit coin. As Lendon puts it:
"The old stories of the Romes, then, are not just a Roman rumination on their aggressive, competitive military ethos, but also a way of worrying at the tension between that ethos and another fundamentals Roman military value, disciplina. 'Discipline,' the flat English translation, ails to convey the full force of this Roman concept. For disciplina was not primarily a system of imposed or felt rules to make an unwarlike people place themselves in danger, to do something unnatural to them. In the old stories the Romans used to think about disciplina, tales like that of the son of Manlius Torquatus, it is conceived primarily as a brake to overly aggressive behavior." . . . . "Roman disciplina was understood to be more a curb than a spur, and it formed an opposed pair with Roman virtus."
I hope this is a good explanation for my opinion, but feel free to ask any questions for clarification if you have them!
Sources:
Adrian Goldsworthy
• "Caesar: Life of a Colossus"
• "In the Name of Rome"
JE Lendon
• "Soldiers & Ghosts: A History of Battle in Classical Intiquity"
Plautus
• "Amphitryon"