Carthage is one of the best factions to play it slowly with careful expansion, if you like that kind of campaign.
From the start it has a very stable economy letting you have strong garrisons in both Iberia and Sicily, decent garrisons in other provinces plus keeping their starting fleet. All of this and you could still gain 6k a turn (may vary with you campaign difficulty) while having Atig, Lilibeo and Hadrumentum at low taxes.
My suggestions are:
- Use the "Carthaginian Army Composition" guide by Trarco to build your armies historically. Its an excellent work done by Trarco and for me is a must for any Carthaginian campaign.
- Until you reach the first reform that unlocks new government buildings don't build Settler Colonies in regions you conquer, unless you know what type of recruitment you can have after the reforms. The colony points you can gain over the full length of the campaign can reach, at best, 250-270 depending of fast you can upgrade Atig, Lilibeo and Hadrumentum to council administration, so they are limited. Build Trade colonies and recruit those beautiful and very useful Ligurian, Iberian and Gallic mercenaries.
- Until you reach the first reform, don't build Supervised Colony gov in your newly conquered regions and instead opt to install an allied government. Supervised colony is limited in terms of infrastructure and recruitment and to upgrade it you have to build Settlers colonies which will be difficult because you will have few colony points in the first 2 to 3 decades. Allied Gov's permits some basic recruitment for garrisons (which can be supplemented with a Trade colony) and gives you more buildings to build, specially roads that are fundamental in some regions (ex.: africa).
- Destroy your supervised colonies gov in korsin and "" and install an allied gov for the reasons above.
- Don't school your young FM in Carthage or they will be elected into Rab Sheni (deputy general) in their second turn after coming of age, even when in peace.
- First time you go to war you will be asked to chose a "War leader" via script. If you say yes your selected FM will be the main general of your army, and elections for Rab Sheni will be available at Carthage. Even if you FM have the trait "Eligble for Rab Mahni" they will not be elected because you have a War Leader. For what I experienced you can have a War leader for each faction you are at war, excluding rebels. If you don't chose a War Leader via script, Election for Rab Mahni can be held at Carthage but are limited for only a few candidates.
- Let the Numidians grow before absorbing them for it creates a nice challenge for you. If not, let them at least conquer the interior regions of africa and let them stay there (preferably then allied with you) unless you want to fight those scripted raids.
In my current campaign I'm taking it slowly and semi following the historical turns of events (fortunately this time Carthage won the first punic war in Sicily
may even call it First Latin War
) and its been a lot of fun. I also like to intervene in external state of affairs which my strong economy and fleet lets me. For example, Macedon was getting stomped by Koinon Hellenon but with my help they are recovering and took Athens recently.
Hope I could help and that you enjoy your campaign.