As now I have a bit more of experience with the mod in general, and armed with the knowledge of how raiding actually works, I decided to give another shot to the horse boys.
Both (successful) recent attempts had the same start - I would take Sigan and move to raid the farmlands in Mauritanea. That added cash would help me to get out of the red real quick (and given how profitable the Conquered Tribe is, plus the general above-average wealth of your core regions, would quickly net me a respectable income), allowing me to build up the bare minimum infrastructure to break out of the North African stranglehold: a port in the capital so I can get a ship and actually move an army out in a speedly fashion.
First attempt, Iberia. I figured if my armies had to be mostly cavalry and VERY light infantry, I should probably go against a people that is a bit short on anti-cav power. I eventually managed to conquer the entire Western side of the Peninsula, but Leusitanians who refused to remain dead, terrible public order, not very profitable provinces, barely adequate allied governments (couldn't institute a single Tributary there, order was this bad) giving me just a handful of questionable infantry to support my cavalry made me eventually grow so frustrated I just give that one up.
Second try, same start, but I decided I would just grab the periphery of the Ptoles. Isles, bother the out of Anatolia, etc. But I also remembered that I could buy some land off the Carthaginians in my last attempt, so I decided, why the hell not? These places are close, so public order and income penalties will be smaller. So I saved up some cash in a few turns and went for my first acquisition, Iykoshim. That was a fantastic buy.
As you can see in the screenshot, the place had FANTASTIC Steppe Nomadism from the get go, and to my shock, despite being a settled region, I could build a Conquered Tribe there just after a few turns as a Tributary (that was quite profitable, btw). This is ing huge. This place is a fantastic source of your good troops that you won't have to sacrifice with Urban Administration, and is a pretty rich city right from the start. Also being between Sigan and your capital, it basically belongs there. And it was pretty cheap too, I think I got it by 8 thousand, being generous, which I quickly regained. So I decided, why not go further?
And so I went.
As you can see, Carthage sold me EVERYTHING that was actually important. The... east-most city is not fantastic, you can get some Lybian troops there, but the same deal as your main roster, so they are not actually contributing anything to solve your frontline/staying power problem. However, there, I noticed you actually get troops out of the Settler Colony. There, just more tribal trash. But, in the two cities...
The very competent and cheap Carthaginian mainstay. And furthermore, if you turn these places into Allied Democracies...
You are never going to run out of infantry again, and can even get the odd Elephant out of the deal. The only purchase that was overall mediocre was the settlement in Sicily (Lilibaeum?). The colony does nothing there, and the allied troops are a mishmash of Greeks and Phoencians in small numbers.
So yeah, with this rooster (and economy) I can easily tackle the big guys out if I want to. It felt kinda cheap though, because Carthage would sell me vital provinces (for them) for values between 8k and 16k, just like nothing. They were EXTREMELY reluctant to sell the isles though, which are nowhere as important as the four cities, so figures, it felt a bit exploity. But I do STRONGLY encourage you to buy (or conquer) Iykoshim.