Alpha Centauri is a really interesting game if you don't mind the old-school graphics and are more interested in the gameplay and lore itself. What made the gameplay more interesting are the very factions themselves and how each one of them is unique in their own way. There are about 7 factions in the original game and 7 in the expansion, the former (no pun intended) I play more often since these factions tend to be more balanced than the new factions. What's more, I also think that they're more memorable than the latter since the original 7 Ideologies tend to be more noticable in our current society rather than the latter.
In regards to how each faction is played, I have personally arranged the original 7 from which is most likely to be played as
Builder (
Wanna be my friend?
) Or Momentum (
NO MERCY 
), Considering that you're playing the unmodded SMAX:
BUILDER
- Morgan Industries

- U.N Peacekeepers

- University of Planet

- Gaia's Stepdaughters

- The Human Hive

- Spartan Federation

- The Lord's Believers

MOMENTUM
Here are the explanations on why their faction sits on where they are on the scale:
Morgan Industries 
Starting Tech:
Industrial BasePreferred Ideology:
Free MarketAnti-Ideology:
PlannedFaction Bonuses:
+1 ECONOMY-1 SUPPORTCommerce Bonus (Inreased values of treaties, pacts and loans)
Bases may not exceed beyond a population of 4 without a HAB COMPLEXThe Ultimate Builder faction out of the original 7. This faction heavily encourages you to use probes rather than attack your enemies head on, as probes do not cost any mineral maintenance and can be equipped with some decent armor. The
-1 SUPPORT means that you won't actually be fielding a large army at all and the HAB COMPLEX limit could actually hinder you if you don't go for
Industrial Automation (Which henceforth unlocks the powerful Supply Crawler and the HAB COMPLEX). On the flip side, he's got
+1 ECONOMY. Once you get to Wealth and Free Market, you will end up with a staggering
+4 ECONOMY and you'll be swimming in loads of energy credits which can be then used to research at a crazy rate like

or imitate the talent bonuses of

through psych boosts. Just be careful going Free Market though, as the
-3 PLANET will kick you hard in the ass should

,

or the local wildlife come knocking at your door. At the same time, any enemies who go against you late game will have to deal with armies of armored probe teams, ready to subvert any unit (except most likely

) foolish enough to step into your corporate borders alone. The commerce bonus also encourages you to be a really nice guy to others as you'll more likely to benefit than them should a treaty of friendship be signed (Commerce Bonus). As much as possible, once you get the opportunity, try to Sign a Treaty of Friendship with other factions. His bonuses on energy credits can be converted into anything on the SE sliders, so he sits as the king on the Builder scale, and at the same time, he sits at the bottom of the Momentum scale due to the SUPPORT penalties. However, it is still a viable option should you go Momentum with

. If you are to go Momentum with this faction , your best bet is to go for Clean Reactors to mitigate the support costs that units usually have. Also, you ought to avoid going Free Market if you are going Momentum with this faction.
U.N Peacekeepers 
Starting tech:
BiogeneticsPreferred Ideology:
DemocracyAnti-Ideology:
Police StateFaction Bonuses:
-1 EFFICIENCYMay exceed HAB COMPLEX limit by 2
Extra Talent every 4 Citizens
Receives double votes in the Planetary CouncilThe most balanced of all the 7 Factions. Don't mind the
-1 EFFICIENCY, as going Democracy remedies that problem. This faction in the end sports no bonuses in regards to social engineering and can be quite versatile in whichever playstyle you go for. A beginner friendly faction since the Extra Talent means that you'll more likely trigger Golden Ages in your bases (Especially with the Human Genome Project which you can start building since you have Biogenetics from the start) and the HAB COMPLEX freedom means you can grow your bases larger than the rest of the 6 factions. The Empath Guild is a must-have for this faction, as once you meet and greet everyone else on Chiron, you can easily forge friendships with the right SE choices; and with the help of the Double U.N votes, you can easily become the planetary governor.
In the scale, he is one step ahead of

on the Momentum Scale as he does not have any militarily crippling penalties (The -1 SUPPORT) but behind

and

since has no bonuses to them either (Whereas

can just research deadly weapons and

can use Mindworms to her advantage). He sits as second to the highest on the Builder scale as his bases tend to become well developed.
University of Planet 
Starting tech:
Information NetworksPreferred Ideology:
KnowledgeAnti-Ideology: Fundamentalism
+2 RESEARCH
-2 PROBEExtra Drone For Every 4 Citizen
Free NETWORK NODE at every base
For Science! A fan favorite among Alpha Centaurians, This outstanding faction boasts an Immense
+2 RESEARCH and a free tech, so you'll most likely eclipse the other factions in that regard if you play the cards correctly. If you find any alien artifacts around Chiron, your best bet is to either link them to your NETWORK NODES or you can use it to complete the heavily coveted Virtual World secret project. That will be your utmost priority since you got those pesky drones around your bases and completing it will mean that your NETWORK NODES now have a double purpose as they now become HOLOGRAM THEATERS as well, reducing the number of drones and eliminating your main weakness. If that ever happens, you'll be nigh unstoppable once you begin researching CONQUER techs. Although the reason why I placed

lower on the Momentum scale is because research bonuses takes some time to develop his army while

can actually capture mindworms at the start of the game. The
-2 PROBE will be one of the things that could haunt

(Especially if

and her
James Bond Priests take their precious time in visiting your ever vulnerable bases) so another important tech to consider here is the Pre-sentient Algorithms, as it unlocks the Hunter-Seeker Algorithm, making Probes useless against

. Also, he is one of the ones most likely to achieve Transcendence, as he can cut through the tech tree like a hot knife through butter. Better techs mean better facilities, therefore, he can actually do a pretty good job in going Builder.
Gaia's Stepdaughters 
Starting tech:
Centauri EcologyPreferred Ideology:
GreenAnti-Ideology:
Free Market+2 EFFICIENCY+1 PLANET
-1 MORALE
-1 POLICECan capture mindworms at the start+2 EFFICIENCY with
+1 PLANET? Hell yes. This faction really has bonuses to both Momentum and Builder factions, making this a really good Hybrid faction. With the
+2 EFFICIENCY, you can go for Green and increase it to
+4 EFFICIENCY, thus netting you a PARADIGM ECONOMY! In any case, you can actually slide your numbers to 100% without any penalty reductions. The
+1 PLANET means you can capture mindworms at the start of the game, thus rendering your
-1 MORALE useless since most of the times, you'll be spending most of your precious time trying to catch
pokemon mindworms all around Chiron. This makes Deirdre a viable faction to go for if you want to rush your enemies early in the game. Not to mention, you can already build formers at the start of the game once you choose the Gaians! Despite her rather peaceful nature story-wise, she can actually be a VERY deadly opponent in the hands of a Momentum human player. The very fact that mindworms IGNORE armor also means that no matter how high their armor is, you CAN have a fighting chance against them (Considering they're not Neural Amp. Tranced/Empaths next to an enemy Sensor).
-1 POLICE could be a bit of an issue, but it can nevertheless be worked around with. A great faction overall when you want a both good economy and a few pets that can be used against traditional opponents.
The Human Hive 
Starting tech:
Doctrine: LoyaltyPreferred Ideology:
Police StateAnti-Ideology:
Democratic+1 INDUSTRY+1 GROWTH
-1 ECONOMYIMMUNITY to EFFICIENCYFree PERIMETER DEFENSE at every baseOne of the first Momentum-oriented factions around Chiron and an outstanding one as well.

likes to build it quick and grow it fast. With the innate
+1 INDUSTRY and
+1 GROWTH, he can develop his bases very quickly and build most facilities right off the bat. Another thing to consider is that he's got free
PERIMETER DEFENSES at every single one of his bases, making early rushes against him a very risky venture. He also starts with Police State free of charge. However, since your
-1 ECONOMY reduces energy income, it will take some time for you to switch to Police State. If you are however able to switch to Police State, you can actually enjoy its benefits and none of its penalties. The same thing can be said for Planned since it has the same penalties in efficiency where

is IMMUNE to it. Even more, the bonuses stack to

's already powerful INDUSTRY, thus turning him into an industrial powerhouse. However, the static EFFICIENCY and
-1 ECONOMY means that you'll be itching for energy credits later in the game, which places him closer in the Momentum scale. Another thing that is unlocked upon researching Doctrine: Loyalty is the Command Nexus Secret Project. This secret project, combined with your innate INDUSTRY bonus, makes you a potential candidate to grab this game changing wonder; as once it gets in your hands, all you need to do is spam units like there's no tomorrow without even spending minerals on building command centers.
Spartan Federation 
Starting tech:
Doctrine: MobilityPreferred Ideology:
PowerAnti-Ideology:
Wealth+2 MORALE+1 POLICE
-1 INDUSTRYPrototype units don't cost extra mineralsSurvival of the fittest. That is the ideology in which the ever militaristic Spartan Federation adheres to. This is even reflected on the bonuses that they get. The
+2 MORALE means that your units already start off with a decent amount of experience in combat and
+1 POLICE means that they will have an easier time quelling off those drones in the bases that they capture. Like

, she is pretty much also a potential Candidate to construct the Command Nexus (hell, this is a MUST have for all Momentum factions), should she find a way to workaround the
-1 INDUSTRY to

's +1/2 INDUSTRY. One fun thing that I did find about

is her formers. Why?
Because even the promotions carry to the formers thus, if one of her formers hit elite,
she literally has a free rover former before fusion reactors at her hands due to the movement bonus elite units have. That's not all, try equipping your formers with armor and try not to laugh as some units get taken down by an
elite former. When the Spartans mean business, they mean it. The freedom to construct prototypes without extra minerals also helps in the conquest victories of

, as units who are completed as prototypes tend to have an innate promotion, which also stacks with the Spartan
+2 MORALE. A heavily Momentum focused faction, since the -1 INDUSTRY could hinder facility construction at some points, this faction likes to play it rough.... But not as rough as the next faction that will follow which is:
The Lord's Believers 
Starting tech:
Social PsychPreferred Ideology:
FundamentalismAnti-Ideology:
Knowledge+2 SUPPORT+1 PROBE
-2 RESEARCH
-1 PLANET+25% bonus when attacking enemies from strength of convictionsDeus Vult! If you like fighting for the cause of God then this faction is definitely for you! If you're that kind of person to hate every single faction on the map, choose

, as the
+2 SUPPORT will end you up covering the map with orange units and the
+25% attack boost means that when your units just so happens to touch theirs and you got that extra move, they're history. One good way to utilize the strengths of

is to play it rough right at the beginning of the game when most factions still has scout patrols to begin with. Your units clearly has the advantage, so if you happen to have a neighbor, then pack your
lasers Holy Bibles, because your
Believers will be having some
vendetta conversion to do, especially if said neighbor is none other than

.
+1 PROBE stacks with the
+2 PROBE boost of Fundamentalism, so your probe teams (Or Priests as I would like to personally call a Believing Probe) will be really damn good at their job. The innate
-2 RESEARCH of

means that once she goes Fundamentalism, Believing researchers suddenly become statues as the
-2 RESEARCH of Fundamentalism stacks with her already low RESEARCH. In that sense, your best way of acquiring new techs is to send your
Probe teams Priests in the
Clandestine acts Holy Pilgrimage of
Tech Stealing The Acquisition of Holy Intellect from
The University Faithless Heathens. The
-1 PLANET is also another bad thing to have though, as once you end up inciting the wrath of

or

you'll end up becoming a
Martyr for your faction.

is not about playing it peaceful, because doing so will mean that she will most likely end up being stuck with sticks and stones while

is already trying to transcend.
The Believers are the ultimate Momentum faction and is really meant to be played that way. The Believer rules go like this: If you do not bully them, they will bully you with their techs. If they do not believe, they die. And if they don't die, you die. It's that simple.
I hope that my Builder-Momentum scale helped

.