Progressing past labourers

With dialogue, ie story mode, which may include the tutorial tech progression seems to be time / event based and you have decreased input as to the pace of events.
If you play without dialogue tech seems to be unlocked on the tech tree.

Food stores and stockpiles

These are linked. The totals are universal among stores. The more you build the larger your capacity. Workers from these stores appear to distribute the items to the production facilities. With too few stores the workers can be overwhelmed.

Vaults

The more vaults you have the higher your capacity for coin. These may also be affiliated with increased revenue, TBC

Military

Invisible Armoury Cap
It seems that troop production from an armoury has an invisible cap. I overcome this cap by building more armouries. Others have suggested demolishing and rebuilding the armoury.

Troop type
With the logistical need to feed your troops outside your territory I would suggest cavalry as ones primary troop type. They can take out a city and be home before lunch. Make archers for your towers. I have not found a need to build walls yet. The best defence is a good (fast) offence.