So a few observations..
Popping the hut undoubtedly right and bad luck versus the barbs...
Stone. The stone for us is a complete red herring. Our next border pop is a long way away (55turns) so forget leveraging it for any early wonders (Henge / Pyramids). If we wanted it quciker we would be settling a very marginal city (deer / stone) when there are far better sites available.
Research post BW. I would look at Agri, AH to Writing as each one is a useful tech by itself with crops to be farmed and Cows/ pigs (later) to be hooked up which will be useful for our next few cities. Before researching the relatively expensive tech of Iron Working I would have a library plus two scientists up in our capital as we will get to IW a lot faster.
I would slip in the wheel only if we have copper on hand so we can hook it up to produce Axemen.
Micro Management. It looks to me as if we we could have switched a citizen to the three hammer hill a couple of turns ago once we hit size 2 . This would have got our worker started a turn earlier and so accelerated our progress slightly. A detailed nit picking MM point but as you go up the difficulty levels it is good for these to become second nature.
SO decisions for the team to discuss
Research path post BW.
Build post WB, Worker Warrior or vice versa?
just to quickly pick up on a couple of points here:
initial setup of the capital is crucial. we should have been working the highest hammer tile immediately to get the WB out ASAP.
we have three options for next build: worker, warrior or WB
on the one hand, warrior might be the best choice: i can't see much land explored so that might be a problem for planning cities.
on the other hand we could build a worker. i'm not leaning towards this one much as there isn't much for him to do apart from build mines and chop forests.
on the (third???) hand, we have an interesting opportunity to grow to size 3 before pumping out the first worker. this has the advantage of added growth and more commerce early on but might come at the price of an earlier settler.
personally i would go straight for another WB, as our worker won't have much to do at the start and i don't think a new warrior is necessary quite yet.
whichever we choose the city setup should be the same: on the first turn, settle the WB and switch the workers around: one to the clams the other to the 3 hammer hill. this will allow Rome to grow to size 3 using a +2 food surplus to coincide with the completion of the WB/warrior if that is chosen. then working 2 clams and the 3 hammer hill, pump out a worker. if we choose the worker option then we should work the same tiles for maximum production/commerce.