Here is 1180 BC same game, I captured 2 cities and when the 3rd one couldnt satify my need for booty i slaughtered them all (was size 1 city and didnt survive the attack).
This is with just 2 horsemen, I am about to finish chopping out the 3rd one and slave out a 4th.
At this point my only problem is making enough archerers to defend the cities I capture!
Details about attacking with horsemen:
Move up next to the city and skip a turn so you have full movement for the attack. If the city has more than 2 defenders you will need an archerer to defend your attackers. Bring your scout along with your horsemen to keep them healed, just remember to not group them as the scout cant keep up with the horse always. (scout is slowed down by hills/forests ect.)
After taking the city, fortify till healed and move archerer in to defend. This healing time usually takes 1 to 3 turns with your medic there.
First promotions should be withdraw 1 and 2, for the first strike immunity. Then i would go for combat 2 and the 25% bonus vs ranged. With those stats you can compete with longbowmen later.
Im currently researching towards alphabet to demand/trade for techs. Isabella infected me with buddism, which is ok since i gain the happiness and diplomacy bonus as i start wiping out the chinese.