Playing on H/H as Scipii, I realized several things.

First, that the chance of SPQR electing one of your family member to be part of their little circle of power in Rome is microscopic. So far only my heir has been elected as the lowest rank (Praetor or something concerning $) and is kicked off the next year, only to be replaced by the Brutii.

Second, equites are pretty useless against long shield cavalry

Third, I think it's best to delay your mission to conquer Carthage for as long as possible. Carthage itself grows like a mofo (+8-9% pop. growth each turn) and doesn't have much of an income, and soon the squalor also increases like a mofo and the income drops like a mofo. I guarantee that it'll start losing 3000 denrarii in no time. I'm having trouble with maintaining it myself. Tried the leave-the-city-then-reconquer-it-and-slaughter-all-those-sorry-asses-inside plan but it backfired. (Carthage returns to Carthigian with full stacks of elephants and Poeni's and long shields)

But if you're good enough, you should be able to re-massacre Carthage over and over and over and over again till those sorry asses stop complaining.

Anyway here's how I did:

Take Syracuse. This seems obvious but move all your units and slaughter the Greeks inside the city, enslave it (to boost income...mmm...denrarii...good) and meanwhile build a milita barrack in Messana to train additional hastaii. Hastaii are your secret weapon in the early game. But Principii are just as good if you can get them.

Then build up an army loaded with Hastaii and your best general, and conquer Lilbayeum (or something) and again, enslave the pop to boost your income.

And now the senate would probably ask you to blockade a few Greek or Macedonian ports over at Asia minor. DO IT. You want the Senate to like you. To love you, to...(go figure)

Meanwhile gather a few hastaii and ship them over to Caralis, the big island just west of your Italian capital (Capua) and besiege it. Take it over. Put a governor in it if you want to make money fast. This island is very crucial to your state finance since when it grows it'll obtain ports and dockyards which in turn will connect trade routes to Capua and Sicily and boost up your economy like a mofo.

Then at this time, the Senate will asks you to conquer the Carthiginan city of Thapsus. Do it. Enslave or masacre the city. (Up to you; I enslaved it) and build pave roads or highways IMMEDIATELY. Africa is vast so you need to save time by moving your legions on highways, not just ordinary roads.

Build up your legions and ship them over to Africa. The Carthaginians will constantly send troops to harass you. Build watchtowers if you like.

If you're lucky, the senate will asks you to conquer Lepics Magna before going onto Carthage. (I wasn't so lucky though) Take it. Late build port to monopolizes your Mediterrean sea trade. (mmm....($)($))

Then it's the final ho-down with might Carthage. Get your best general, get as many hastaii and roman archers and any other experienced troops you can spare, and besiege the city.

Usually with a hugh city like Carthage it'll take it 8 full turns to surrender. HOWEVER if there are roaming carthaginian armies outside the city they might attempt to break up the siege and attack you. This is to your advantage. Use it wisely. I found out that my hastaii and principii are no match even against their Libyen Spearmen on the wall. So it's better to pepper the living shizs out of them with pila and missiles out on the open and THEN slaughter them.

After Carthage is yours, just sit back and relax for a bit. (I'm still coming up wit the second half of this strategy, heheh)

Peace