a mosaic of farmers pressing olives to make olive oil
Most people in the Roman world were farmers. Some of the people who worked on farms were slaves, but most of them were free. They grew wheat and barley and olives and grapes and apples, onions and celery. Mostly they sold what they grew in markets in the towns, and bought food in the market to eat, as most farmers do today. And they paid taxes, as farmers do today. Roman farmers paid their taxes partly in money and partly in food.
Roman bronze coins
A lot of these farmers lived in small villages, but a lot of them also lived in bigger towns, and walked out to their fields every day. In villages, people mostly lived in mud-brick apartment buildings with courtyards, and they did their cooking on braziers in the courtyards. People who lived in town often lived in small apartments, with no courtyards, and didn't have kitchens, so they bought most of their food from street vendors or in fast food restaurants.
a mosaic of Roman trading ships
Rich people and their slaves also lived in the towns. Some of these rich people owned a lot of land, and rented it out to poorer farmers, or made their slaves farm it. Some of the rich people ran businesses, making clothes or tools in factories. Some poorer men in the towns taught school, or were doctors, or carried water, or ran bakeries, or begged. Women in the towns sold things in stores, or did spinning or embroidery, or worked as wet-nurses, or begged. Women didn't generally teach school in ancient Rome. Many of these people working in towns were also slaves.
a Roman amphora,
used as a shipping container
Roman people didn't have to just buy things that were made locally. Traders sailed across the Mediterranean Sea bringing papyrus from Egypt, glass from Phoenicia, pork sausage and salt from Austria, tin from England, fish sauce and cooking pots and dishes from North Africa, and olive oil from Spain. Even ordinary farmers could afford a lot of these things.
Some traders went even further, into the Indian Ocean or across West Asia, and traded with people in India or in West Asia to get Indian cotton, pepper, cinnamon and other spices, and even silk that came all the way from China. But these things were very expensive, and only very rich people could afford them.
To find out more about the Roman economy, check out these books from Amazon or from your library:
Eyewitness: Ancient Rome, by Simon James (2004). For kids.
Archaeology of the Roman Economy, by Kevin Greene (1991). An expert, but a good writer. Greene, like many archaeologists, comes down on the side of a market economy.
The Roman Empire: Economy, Society and Culture, by Peter Garnsey and Richard Saller (1987). Two experts, but their writing is easy enough for high schoolers. By Finley's students, and basically on Finley's side.
The Ancient Economy, by Moses Finley (1973, updated edition 1999). The book that first started this argument. Basically on the side of "consumer cities" and people farming their own food. The writing is, again, clear and simple.