Nice opening. I'd say you're off to an excellent start.
If vassals are allowed I'd say Feudalism has to become an
immediate priority...
you only get 6 cities, but your vassals could help you fill up the rest of the land so you don't have to keep re-conquering the same territory, plus keep up in tech... and eventually they may even start contributing units to the war effort.
As far as next target goes... I would probably hit Gilgamesh. Vultures are basically equivalent to Axemen against Praets (their big benefit is being tougher against archers and chariots, which doesn't bother you ). He's one of your strongest opponents, he's teching quickly, he's nearby, and he looks silly. I strongly recommend trying to get at least 2 more cities out of that war - last game I was recommending you hold out for a really great 4th city since you only got 4, but seeing the way that game played out convinced me I was wrong to do so, and it's probably better to just get as many reasonably good cities as you can as fast as you can in with a restriction on number of cities. Make sure to either conquer or found a coastal city at some point, in case this Pangaea has some of those dinky little offshore islands to worry about.
Side note 1: I would have laughed quite a bit if you'd ended up with no iron and these restrictions. Fortunately for the continuation of this game, the random number generator didn't hate you that much.
Side note 2: Axemen are stronger attacking against praets; vultures are stronger defending against praets.
On attack, with combat 1 for both units...
Axeman has strength 5 * (1 + 0.1) = 5.5; praet has strength 8 / (1 - 0.1 + 0.5) = 5.71. Ratio is 5.71/5.5 = 1.04 in favor of Praet.
Vulture has strength 6 * (1 + 0.1) = 6.6; praet has strength 8 / (1 - 0.1 + 0.25) = 6.96. Ratio is 6.96/6.6 = 1.05 in favor of Praet.
On defense, with Combat I for both units...
Praet has strength 8 * (1 + 0.1) = 8.8. Axeman has strength 5 * (1 + 0.1 + 0.5) = 8. Ratio is 1.1 in favor of Praet.
Praet has strength 8 * (1 + 0.1) = 8.8. Vulture has strength 6 * (1 + 0.1 + 0.25) = 8.35. Ratio is 1.05 in favor of Praet.
Check out the Combat Explained article -
http://forums.civfanatics.com/showthread.php?t=137615 - if you're curious where those formulae came from.