My preference would be towards a more "modern" style of government due to the fact that to be really involved in the current form requires at least some degree of familiarization with mythology and tradition, and a willingness to use that "in character" to some degree. Now, I'm not opposed to hittin' the books and educating myself, but it may serve to hamper our desire for an active government.
Also, even though it sounds exciting, I don't like the idea of being able to challenge council members through the dueling process on a whim. The last thing we need in the midst of any serious issue is a drastic leadership change that divides the allegiance of the population and weakens the region. Unless there is some sort of serious wrongdoing, leaders should stay in place until elections say otherwise.
For that reason I propose a simplified republican (little r) system. We could have a President (Delegate) Prime Minister (Founder) and a combined legislative/judicial system made up representatives elected by the people (1 rep per 10 nations perhaps?). Then we could have cabinet posts as needed, which should be minimal unless we intend to do alot of roleplay, or defending action (both seem somewhat unlikely, but who knows?). Those posts would probably consist of SecState and SecDef.
Now get posting and lets form our government!!! haha