All right, looked at the save too, here are my thoughts. Let me start with two screenshots:
We have four horse units, two melee combat units and an archer, as well as two triremes. When we go against our next targets, we have to consider that the patch has nerfed our horses. We shouldn't rely on them as main attack force anymore (although when upgraded to knights they will still be very powerful). We have only two iron left currently. I think its a good idea to build two ballistae (our unique catapults) with the remaining iron, to get some siege support.
We clearly are not that weak, judging from the soldiers rating
we also have the lead in land area and crop yield, which should help us to catch up in population. I'm wondering why we have so low production, but our cities are still developing and I think it'll be ok in the long run.
Suggested city builds (after they complete what they're building now)
Rome:
- Watermill (->Production!)
- Ballista
- University
Insert the national college once available (in 15 turns), same for other national wonders.
Antium:
- Circus
- Ballista
Cumae:
- Market
- Perhaps a spearman/pikeman in case we have to face horses?
Neapolis, Ravenna: Collosseum, Market (to be able to build the other two national wonders)
Note that we should not build more units immediately, before we know where the other civs are.
Alliances
We should also immediately ally with Lhasa. Friend status is nice but doesn't help us all that much! I'm fine with spending 500g for now, that will give us 72 turns of ally status if I count right (due to patronage
Btw. all city states give 65 influence for 500g and 130 influence for 1000g, so there's no advantage to paying the larger amount.
Tech:
I agree with going for chivalry next. Then we have to choose tho, banks would be great (could also build forbidden palace), but we could also go for metal casting -> steel (12 turns total), longswordmen would help us immensely in the coming wars I think! Metal casting would also open up machinery (-> crossbowmen).
Social policies
I checked, we don't have discipline from honor yet (+15% combat str when another unit is adjacent). Could pick that up, I'm not sure how important it will be, considering we are pretty good in power currently.
I still would like to continue down the commerce tree then, or do you prefer other things (we will also have rationalism and freedom available once we finish astronomy and enter the renaissance era!)?
New cities:
I would like to hold off building more cities, until we finish the national wonders. Thats up for discussion of course.