I think we should beeline to Republic. Republic permits greater commerce and has lower corruption than most other governments, including Monarchy. Commerce is the key to wealth, permitting more trade, faster scientific advances, and more production (contributing cash towards completing city improvements or military units become easier and a viable strategy). Under Republic we will want to build marketplaces in large cities (except for those that are hopelessly corrupt) and acquire more luxuries (either through trade or war). Luxuries and judicial use of the slider are the keys to success under Republic.
Several citizens make the point that it can be problematic to maintain happiness under Republic if we have too many troops. This is an excellent point, and well have to plan to overcome it. It doesnt justify favoring Monarchy (which allows the use of troops as military police) over Republic, however. Under Republic, having more cities it makes it easier to maintain a larger military, so we will want to grow. As described above, more luxuries and use of the slider also makes maintaining happiness straightforward (although a healthy commerce is a necessity). We will want to wait to time our revolt to Republic until we have a decent-sized, productive civilization. We should have that towards the last third of the Ancient Age.
One of the perceived advantages of Monarchy the ability to use troops as military police is actually a major disadvantage. First, using troops to maintain happiness rather than using the slider may encourage less diligent development of our cities. Second, there is a cost to using those troops. Although their maintenance is free, we have to keep them in cities. Having troops in cities far from our borders means theyre useless to defend against an attack on our borders. More significantly, should we decide to go to war, we cant use those troops that are on MP duty unless we want to increase unhappiness. Although Monarchy has less war weariness than Republic, as long as a Republican war doesnt last too long (over 20 turns), war weariness doesnt become a big problem.
Last, we are the citizens of Fantannia! Do we want the jackboots of an authoritarian military on our necks? The military should be the instrument of the policy goals of Fantanian citizens; the function of the military shouldnt be to pacify free Fantannians!