Heres the final version of the rules that I think would be suitable for the game.
History:
We had a ruler that collected different brave people from the surrounding areas and united them by building a city Nessos. After he died the people thought that no other family leader deserves to be the king after that hero and that none of the family leaders deserves to be the king more than the other anyway. So people decided on the republican sort of government. Das how about a story on that?

(something like beginning of the history of the Rome. I can retell it if you want)
So now to the stats and rules
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THE GOVERNMENT:
The government is made up of 3 branches: executive, legislative and juridical.
Legislative is made up of the Senate (for now only the senate).
The senate consists of all heads of families (players). It can make up legislation and withdraw already passed laws.
Laws pass with 60% majority and can be withdrawn with 80% majority. Tribunes that speak for the people can be elected later. And I assume we are all patricians, right?
Executive branch is for now represented by the 2 councils, elected for 1 year. They have the power of kings and enforce the rule of the Senate of the people. In extreme times the senate can vote on electing a Dictator that rules for 1/2 a year with unlimited power. Councils are supposed to head the armies in times of war. Other representatives of the executive power can be added after some gameplay. Councils have virtually unlimited power so its good to be them. There should be laws restricting the right to be councils.
Juridical power is represented by 3 players. Theres a judge a persecutor and a defender. Their roles are clear. Any player can accuse the other player of anything and if they judge accepts they can be taken to court. If the accuser is proved to be wrong he pays a huge fine. All 3 juridical power representatives are elected for 3 year period.
Anything that your state does in game happens in the name of the people and the Senate. So the senate is theoretically the highest institution. [We might want to create a separate thread for government matters]
Also:
RELIGION
One player could be (or a NPC) a Head Priest responsible for interpreting the Gods will and blessing and not-blessing some actions of government. (This could be determined by random events). Oracle could also be added in the future.
Possible Laws:
Reorganise and train armies
Create new government posts
Councils can distribute the plunder among warriors or give it to the treasury
STATS
Our people are divided into families. Each family has their personal stats.
Family:
- name of family/player
- Number of able men. These can back you up in almost anything. Able means that they can work and fight if necessary.
- Coins: money that the family has
Wealth: any other goods that the family possesses or shares of city production
A special parameter could be for heros names and/or rewards gained by the family like triumphs
A family could have clients (dependant people from plebs). Those could also play a role and be in stats.
City stats:
City stats is the main stat of the country. At the beginning we will have only one city and this city is our only force. With time we could expand and make other cities allied with us but it is in Nessos that everything is concentrated.
Population excluding the family members
City Treasury (Coins) amount of coins in city treasury
Garrison harboured (explained below)
Production (explained below)
Production:
Heres the new bit. Its easier to invent than explain. Technically a city produces lots of things: war goods, food, wood, ships etc. All those goods will be very difficult to have in game and manage properly. Instead we introduce the money equivalent. For example Nessos could produce 25003 wroth of food (in coins). With me? Ok so now we can use this in barter like change 20000 worth of foods for the same worth of military weaponry. (I of course assume that the relative prices are always the same). This way we can exchange goods without actually having a stat for each and every needed good. Now. Who produces all this? Of course it the city. But with time influential families might buy some of production. Some buy land and therefore buy peasant business. These are represented in %, like shares. For example Crassius family could buy 3% of the citys farms and get the revenue from it each turn. Of course buying it would be very expensive. Of course production can decrease and increase depending if you pour money to its development or not. Wars and economic booms also could affect production.
% of production merely means that X% are working for a specific owner. For example: 45% city 13% Crassuis family, 12% Nessos City 30% Tarion family.
Again there will be a great number of different industries that provide different goods:
Peasantry and farming, mines, military production, smithing, pottery, construction, commodity warehouses, winery, shipbuilding, cattle-raising and maybe etc. Some cities would not have all industries. Except for shipbuilding cities would not give actuall production, everything will be measured in coin equivalent. All coins go to their respective owners. I hope you are still with me

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City Example
Name: Nola
Population: 34500
Treasury: 234000 coins (well think of a name for coins)
Industries:
Peasantry: 23000 worth/ 1200 annual income/ 93% city 5% Nessos 2% Crassius family
Winemaking: 23000 worth/ 1200 annual income/ 50% city 25% Cornius Family 25% Crassius family
Military Production: etc
Trade Income? 3400 coins (NOT A PRODUCTION)
Garrison: 2300 noble horsemen, 6700 legionnaires/ 25 triremes 300 seamen
Other Possessions: 2300 slaves? 20 trade ships (or move them to garrison)
Oh yeah cities can own part of other cities production too. Like IRL.
Should slaves be in game as well?
IMPORTANT:
1. There should be a post explaining the roles of each governmental post especially if we create one and this post could also change. This post could also be used to describe military units, ships and other things.
2. This NES is about people. Everything is made up of them. Ships have seamen; ballistas have men who serve them. This should not be forgotten and used in game. So when building triremes remember that they need man also.
Possible Example of Fleet:
Fleet Name: Crassius Fleet
Ships: 143 Triremes
Seamen: 3501 seamen/ 150 sea legionnaires
Cargo: 3000 troopers, 12000 coins
P.S. I did not make any changes to the map and armies so these stay as they were in my previous post.
So this is more or less how I picture the rules. If anything is not clear please ask and please make comments. They are vital and if I dont get them Ill move on to something else.