You may want to start with a Catholic textbook on political philosophy. Ot simply with theire entries in the Catholic Encyclopaedia, those are liable to be extensive and well referenced. Not unbiased, though, you'll need something else to work with. But they should give you some sources and starting points.
Augustine's work is interesting because he so totally divorces the civitas Dei from the civitas terrena (he would, though). That makes sense mostly from his perspective of the total collapse of Roman imperial power. De Civitate Dei is what you want to read, if you have the time to do it.
Meanwhile, Thomas Aquinas writes from a position of having witnessed the imperial papacy and its failure. His ideas on the status of secular power are informed by a very different idea of what the church is. The Summa THeologica is probably too long to read in its entirety.