Five hundred years ago, a world-spanning, decades-long war triggered a planet-wide apocalypse. Survivors from the warring countries had to cluster and work together to survive. Survivors were also constantly defending themselves from hordes of rogue monsters left over from the military efforts of one collapsed empire. After a decade of desperately fighting for survival, the apocalyptic conditions are ended, someone finds (literally overnight) the key to getting rid of all of the rogue monsters, and civilization starts to pick itself back up again. The battered survivors, who've been pretty traumatized by war and a near-constant state of siege and who've had to overcome former national boundaries anyway, are led by people who take this opportunity to found a unified world government in the hopes of ushering in permanent peace. They have distance travel and communication technology back within a few years, so the "world" part isn't much of an issue even as people re-disperse, and the surviving population was probably under a million.
It's been five hundred years. There have been a few minor rebellions, but nothing major and several of them were closer to waves of unrest than fighting. Weapons technology beyond the individual arm is heavily restricted, although the "everyone has to be able to fight to survive" culture has been idealized and lingered in a recreational arms-friendly culture like you see in parts of the US, albeit with more emphasis on hand weapons and less on firearms and without the inherent anti-government sentiment. Nobody's found or even imagined aliens; this world is all there is. There aren't any external threats to worry about, just internal.
What kind of military/peacekeeping/armed police forces might such a world be likely to have, and how large might they be (relative to the population)? Alternately, what kinds of political or social factors would drive the "need" end of the decision-making? For example: maintaining a large inventory of high-tech artillery seems unlikely because the maintenance costs are non-trivial and the visible benefit to society is very low. But having some large-scale weaponry is useful in the rare rebellion scenario-- how might a government decide what's "enough"?
I realize there's a range of answers, and a military police state will, of course, look different than a hippie utopia; the society is going to be somewhere in the middle and (for simplicity) bear a surface resemblance to a modern Western democracy. The reasoning behind answers is therefore especially appreciated so that I can decide where on the spectrum I should put the society and government policies in order to support both a civilian life that takes peace utterly for granted and an elite clique plotting coups using recreated mega weapons.
(I'm also willing to take "Your scenario is totally unbelievable from a societal perspective, and here's why", although that may result in follow-up questions later.)