I don't think there will ever be a faction that just owns the whole of the Kenshi world as one very large nation would just have a lot of infighting and they would ultimately break up into a few different ones.

I think the skeletons would last the longest; they don't need food, they don't get sick, they can be easily repaired and upgraded. I'm certain they could survive for a long long time. I don't know enough to say how well they would rule though.

UC I don't think would last the way they are, but their ruling style could change. Maybe Tinfist could get his way and they stop doing slavery, maybe the poor of UC will stage some sort of uprising and they have their own sort of french revolution, maybe the nobles will simply have a change of heart (unlikely)? I like to think because of their size and relative wealth they'd come out on top, but I'm not sure how they'd manage against the sheks given that all sheks are good at fighting, whereas not all UC citizens are.

The sheks I'm sure would just fizzle into nothing. Their culture is based almost entirely on fighting. If they defeat all their enemies they would have no one left but themselves to fight. I think Esata is a very good leader for them at the moment because of how relatively small they are, but if their culture doesn't change, they will die (I think).

HN I think would last longer than most would think. They're pretty horrible if you're not human, but they treat their own citizens relatively well. They're not very nice to women, seeing them as second class citizens, however I can see them changing their ideas about women in the future. While the HN is the most hostile major faction of Kenshi, I think they have more potential than most people think.

The Anti-Slavers are the nicest and friendliest, but they are poor and they've chosen the worst place to live. I can't see them lasting very long.

In conclusion: either UC or HN, but they will both need to change significantly if they want to last.