On the question of war, and how to go about it, I agree totally that the Great Lighthouse is more important than the Statue of Zeus. Far more important, in fact. However, it is not an either/or proposition but rather a question of timing. We are planning to take both Istanbul and Carthage. In fact, we will be at war continuously until we have taken the entire world.
We should make our war plans on the basis of how best to achieve our plans of taking over the world,
not in terms of which enemy is the weakest. We have no reason to fear anyone. We already have trebs and pikes and soon will have

and a Golden Age. Nothing can stand in front of us.
The main reason to take Carthage first is to get those ACs into our hands instead of the hands of the enemy.
Today, I would guess that there are 2-3 regular Numidians in Carthage plus possibly an archer. The city has been in Wonder-building mode since it was size one and I doubt that there are more than that. Three berserks, and three trebs should be able to take it without problems. Drop an amphibious force two squares away and grab it. Check this guess if you wish; we are currently running a positive economy and probably will be for a long time to come.
In contrast, let's say that the Turkey-first route takes 20 additional turns to get to Carthage. During that period, the city will have built 4 ACs. We will have to amass a force which is twice as big in order to take them out (because of the extra HP, an AC is almost as difficult as a Numidian). Let's say killing them costs a berserk . Those four ACs could have been ours. That's five units wasted, units which we could be using to take out our other enemies. So, tactically, taking Carthage first is clearly superior. Five first-class units is nothing to sneeze at.
Another consideration: Carthage is our fastest route to a fourth lux. In this department: we currently have Dyes, Ivory and Incense. Carthage gives us Silks. Istanbul gives us Spices. Spain has Furs and Gems while the Celts have Wine and Wool.
I would argue that it is better strategically too. Waiting doesn't even get us to the New World faster! Our route to our new home in CelticAmerica lies through Carthage and Spain.
If the purpose of this game was conquest, I have no doubt what my course of action would be. I would grab both Carthage and Istanbul as fast as I could with amphibious attacks. Then a force would strike out from Carthage towards Spain while new units are being built back home to take out the home continent.
This might even be the best course of action as it is. It's certainly worth discussing. Berserks are slow and it will take time to get them to the front. Galleys help, it's true. But we don't want to build more of those than absolutely necessary. This, BTW, is also our fastest route to five luxes and we won't get more until Magnetism.
Perhaps I'm stretching a bit with this thought, but it would be nice to take Entremont before Education to get those nice free border expansions all over the place. It's probably not reasonable to hope for it, as we are only five techs away, (Gunpowder, Chemistry, Metallurgy, Monotheism and Theology) but one thing is sure: the only way to get there is through Carthage.
Summary
The
first two cities we should take are Carthage and Istanbul.
Carthage because:
1. It will have the Statue of Zeus.
2. It gives us a fourth lux.
3. It is on the route to Spain and CeltAmerica.
Istanbul because:
1. It has the Great Lighthouse, which opens the route to S and C/A.
2. It gives us a fifth lux. A cash-rushed harbour might be a good investment.
Once those cities are taken, our strike should be towards Spain. Hit hard. Hit everywhere. The Mongols are of no interest. They can be taken at our leisure. In fact, the rest of the home continent is of no interest. The entire thing can be taken whenever we want.
Edit: if we do adopt this plan then:
1. We should take whatever we can get from the Celts. They aren't going to be around long and grabbing their gpt gets us something while simultaneously reducing their capacity to research.
2. We could bring the Mongols into the wars if we choose. It's probably a good idea. I'd suggest pitting them against the Turks. We'll have enough troops marching through Carthage to keep Hannibal in hand, but an attack on Istanbul could be annoying.