I might suggest you take a look at David Weber's "Honor Harrington" series. It's technically milscifi, but it's mostly about the characters' evolutions, and the mechanics of government society and the military (not in that order -- as the series progresses, the scope gets bigger as the main character rises in the hierarchy, and has more visibility of it all).
On Basilisk Station is the first in that series, I think it has a lot to offer even the militarily disinterested. That title, at least, is in the Baen Free Library, with all the benefits that go along with it.
Besides, David Weber appears to be incapable of writing bad stuff. You may decide you're not interested in the subject matter, but his style is quite good, IMHO.