The most prolific Politics & War guides often contradict one another with regards to the "best" approach to building your new nation. Some say to buy four cities as soon as you can. Others say to wait until your first three are at a certain level. Still other guides suggest a mix of both. Rather than provide any suggestions here, what I'll do instead is offer you numbers in order to make your own decisions.

Keeping in mind that new nations typically don't reach a score of 200 without being raided at least once, it's important to note that Nation Score represents a distinct tier. Raising your score is straight-forward, but becomes exponentially more expensive the larger you grow. There are several factors which influence your score such as your military units, but the two biggest influences in the beginning are your Infrastructure and City scores. In the final equation, Total Nation Infrastructure is divided by 20 and added together with your City score which is represented as (N-1)*25 where N is the number of cities in your nation. No matter how much you pay for it, every 500 infrastructure will increase you Nation Score by 25 points. Every additional city you purchase will also increase your Score by 25 points. It follows that a newly-purchased city brought up to 500 infrastructure will increase your Nation Score by 50 points total.

Assuming you keep your land in proportion to your infrastructure levels (and you must to keep disease and density low), a newly purchased city will always require 480 land and 490 infrastructure to fully "tech up" to tier 1 (500 Inf | 500 Land). At $23000 for 480 land and $323547.87 for 490 infrastructure (w/ gov bonus), it only takes $346547.87 to tech up any newly purchased city to tier 1.

The following table is provided to illustrate costs required in order to tech each subsequent city to tier 1 (including cost of the city); The first equation is with the infrastructure bonus. The second equation is if you had the city bonus. You can only have one government type at a time and can only switch every 5 days. Each t1 city adds 50pts to your Nation Score as well as provides you with 10 improvement slots and ~45,000 population (additional income).

                With Autocracy                    |       With Republic                       |         Savings
--------------------------------------------------|-------------------------------------------|-----------------------------------------
City 2 - $225000.00 + $346547.87 = $571547.87     | $213750.00 + $363576.71 = $577326.71      | +$5778.84 with Autocracy
City 3 - $425000.00 + $346547.87 = $771547.87     | $403750.00 + $363576.71 = $767326.71      | +$4221.16 with Republic
City 4 - $925000.00 + $346547.87 = $1271547.87    | $878750.00 + $363576.71 = $1242326.71     | +$29221.16 with Republic
City 5 - $2025000.00 + $346547.87 = $2371547.87   | $1923750.00 + $363576.71 = $2287326.71    | +$84221.16 with Republic

As you can see, teching cities 3 - 5 to tier 1 becomes more expensive to do with Autocratic governments. For the biggest savings, purchase these cities with Republic. The final costs above also include the [constant] cost of teching each city up to tier 1 (500 INF | 500 LAND), with each equation taking into consideration your government type and its respective savings.

Assuming you are at 500 INF | 500 LAND with 3 cities, you are firmly rooted in what is often called "tier 1". Your Nation Score might range anywhere between 150 to 314.1 (depending upon which military improvements you purchased). 314.1 represents the highest possible score you can attain with 3 cities @ 500 INF. Once you 'tech up' your first three cities to t1 infrastructure levels your base Score will be 150 and you'll have 30 improvement slots available. Assuming you were to buy ONLY military improvements, you could boost your Score up to an additional 164.1 depending on which military improvements (and units) you purchase. A city can have 5 barracks, factories, and air bases but only 3 drydocks. However each military unit is worth a distinct point value. The equation:

Nation Score = (Infrastructure / 20) + ((Cities-1)*25) + (Soldiers * 0.0005) + (Tanks * 0.02) + (Aircraft * 0.2) + (Ships * 1.5)

That means each military improvement, once fully filled, provides a certain maximum score boost depending on its unit type. Those scores are calculated as follows:

BUILDING | MAX  | Score
Barracks - 5000 - 1.5
Factory  - 250  - 5.0
Air Base -  18  - 3.6
Drydock  -  5   - 7.5

Assuming you purchased only those military improvements which garnered the highest score, your 10 slots would be filled with 3 drydocks (22.5pts), 5 factories (25pts), and 2 air bases (7.2pts); with these improvements, each city would add to your score an additional 54.7 points, multiplied three times for each city for 164.1 points on top of your base Infrastructure/City score of 150 for a total of 314.1.

There are two large issues for a nation of this setup, however: it is not cost-effective and in fact will run a large deficit. Unit upkeep in peacetime alone would be $297750.00 dollars which is far more than the revenue 45k people per city bring in. The other problem is that this loadout, although providing you with the highest score possible on three cities, is not tactically sound without infantry (which receive a dramatic bonus from tanks needed to achieve ground superiority in battles). So while 314 Nation Score is possible for a 3-city nation, it is likely a rare sight.

------------Tier 2 And Beyond-------------
This is pretty structured territory. Many of the guides specify that going above 500 INF marks a distinct 'threshold' of tiered nations. It also marks the moment your city requires 2 power improvements in order to power the rest. We'll call cities between 501 - 999 INF "tier 2" from now on. Remember to buy 500 more land to bring your city to 1000 square miles. The improvements you purchase along the way will be contingent upon what kind of nation you want to build. Although efficiency demands that you focus and specialize based on your resources and your ambitions, the Politics & War is built in such a way that all nations can access all gameplay elements.

From 500 infrastructure to 600 = $195842.39  |  $206149.88
From 600 to 700 =                $268872.64  |  $283023.83
From 700 to 800 =                $354696.53  |  $373364.76
From 800 to 900 =                $453213.86  |  $477067.22
From 900 to 100 =                $564338.75  |  $594040.79
Total =                         $1836964.17  | $1933646.48

Assuming you purchase each 100 INF with the Autocracy government, you'll save $96682.31. Keep this cost in mind when purchasing your next batch of infrastructure. 500 land will cost you an additional $255400.00. Remember that you need to increase your square mileage as you increase your population. Batches of 500 land are the most cost-effective and will save you the most money.