My family are from Northern Portugal, and I look more French than Portuguese. I also have little bits of DNA from the British Isles, Italy, and France/Germany.
I want to eat like my ancestors did to see how it would affect my health. What would have been common foods during the middle ages? What about during the visigothic era? And how did the Roman's eat during their time? I've heard of Roman's using extended fasting as a treatment for different mental and physical illnesses. Was bread always a staple? What about red wine?
That's a lot of stuff to cover! Not only for the sheer number of questions, but also the geography.
Everyone ate at least slightly differently depending on where they lived in medieval times and prior, and what they had access to depended on their wealth. To give two drastically different examples, let's discuss the peasant vs. wealthy diet of Britain and Italy first.
In almost all civilizations (excluding ones in extremely unusual areas like isolated islands or the Inuit on frozen tundras), grain would be the staple food and make up the majority of the calories in a peasant's diet. Exactly what grain this was and how it was prepared varied depending on the location and time period.
In England, the staple grain was usually wheat (rye and oats were preferred for animal feed and barley for brewing beer, but obviously in trying times people would eat them as well) either baked into bread or cooked into porridge. This would be supplemented by whatever vegetables were available (such as purple carrots, turnips, onions, and parsnips) and meat and cheese when possible. Meat was expensive and would often be added in small amounts, more for flavor than a serious contributor of calories. Most meat and fish accessible by peasants would be preserved with salt, made into sausages, smoking, or drying; those who did slaughter animals would often sell the choicest cuts at the market and preserve some for themselves. Milk was rarely drank fresh due to how quickly it expired and was almost always turned into cheese and butter, both for sale and personal consumption by the farmers. Flavorings would generally be locally gathered herbs, as spices were quite expensive. Cane sugar was basically non-existent in their diets, but honey was available as a sweetener and you could add locally gathered fruits as well.
Italian peasants likewise had wheat (usually durum), but they also had access to rice starting in the 14th century thanks to Italy's important location on the Mediterranean for trade. The peasant diet wasn't too far off from the English, with the major addition of pasta (made from both rice and durum wheat) and rice dishes when it became available in southern Italy.
You'd see a big difference in beverages, however. Contrary to common belief, water was the regular drink. You'll see people claiming that medieval water sources was so contaminated that everyone would just drink alcohol all the time to avoid poisoning themselves, but that's a myth. Of course medieval people knew when water was bad! Of course they knew not to dump all their poop in the river they gathered water from! Alcohol was the drink of choice when available for all ages because it added calories and flavor to the diet, in addition to a mild buzz. You wouldn't really see flavored non-alcoholic drinks in this time, as ingredients like fruit would be too valuable to waste on drinks.
The usual alcoholic beverage depended on where you lived. In colder climates like England and Scandinavia, beer or ale was the usual choice; mead was a special beverage usually used for celebratory purposes due to the expense of honey over grain. While hops were known for centuries in the middle ages, they spread relatively slowly and were still uncommon in England in the 14th century. Beer was usually flavored and preserved with gruit, a mixture of various botanicals. Wine was the preferred alcoholic beverage in Mediterranean countries like Italy, as wine was produced there and cheap to purchase locally.
For the nobility, you've got access to all sorts of stuff that the peasants don't! You've got all the spices, sugar, and salt you want, which means you want to use a lot of them whenever possible. Medieval medical and dietary knowledge was based on the idea of "humors" that had to be kept in balance in the body to avoid illness, and every type of food and spice had its own properties like "dry" or "hot" that had to be balanced to stay healthy. This leads to some odd pairings and substitutions in recipes that don't make sense in terms of taste but made sense as medical advice. The base ingredients were often covered in sauces and flavorings until they were almost totally lost in garnish, with a sort of general sweet and sour taste for a lot of dishes thanks to the combined use of sugar and vinegar.
Access to imports and money also meant access to products that peasants rarely or never saw, like exotic citrus fruits and freshly slaughtered meat that hadn't been doused in salt. Nobles in beer-drinking areas had access to imported wine and would often prefer to drink it over local beer.
In regards to Ancient Rome, many of the foodstuffs that we associate with modern Italian cuisine (tomatoes and chili peppers, especially) were completely unknown due to being native to the Americas. Much like in medieval times, the ingredients you used depended on your wealth: the wealthy had access to imports in addition to native food. Fortunately for the historical record, writers like Pliny the Elder, Horace, and Cato recorded much of the people's diet.
The usual staple meal of a Roman peasant or city-dweller was puls, a simple wheat porridge augmented with vegetables, cheese, and meat when available. Bread was also available in many different forms, including soft and sweet breads with fruit and honey for the upper classes. Early forms of pasta existed, such as lagana made by rolling out flat dough into sheets. As was common until the past 100 or so years, most meat seen by the lower classes was preserved in the form of sausages and salted or dried meat. The most common ingredient in cooking among all classes was likely olive oil.
One unusual aspect of living in a Roman city is that many of the lower classes didn't cook! Roman citizens (especially in Rome itself) usually lived in insulae, basically small apartment buildings, and only the wealthy had an individual house (a domus) with a kitchen and staff to cook. Apartment-dwellers would often have a charcoal brazier, but it was dangerous to use inside. More commonly they would purchase food from a variety of street stands and restaurants.
A popina was an establishment (usually open 24/7 or close to it) that sold simple foods like porridge, sausages, fish wrapped in parchment, and chickpeas. They also provided an easy place for illegal gambling or for prostitutes to meet clients. Popinae were the usual meeting places of the lower classes outside of the home, including off-duty slaves, which gave them a poor reputation. Tabernae and thermopolia sold all of the above as well as prepared dishes like stews, meatballs, and roasts. Tabernae were frequented by all levels of society, as they were often located near business and entertainment centers and provided an easy place to stop for lunch and socializing.
The primary drink for all classes was wine in some form, as it was produced all across the empire. Winemaking was a mature industry during the days of the Empire, with wines from different regions having their own reputations, styles, and ever-changing popularity just like today. White, red, and rose wines were all common; rose may have been the most common, as it's the simplest to make (dark and rich reds require you to engage in extra maceration and a longer production period to fully infuse the compounds from the grape skins, while whites require you to skin the grapes first). Falernian wine is the most famous of Roman wines, though its popularity changed with time; Falernian aged as long as 200 years was drank, though Pliny admitted that it was so thick and highly concentrated that it was almost undrinkable. And also like in real life, counterfeit Falernian was rampant!
Wine was commonly adulterated for flavoring and preservation. On the positive side, you had honey wine (mulsum) and spiced wine (conditum). On the negative side, you could find seawater, chalk, marble, and pitch.
Wine was typically watered down at a 3:1 ratio of water to wine before drinking, as it was intended for hydration when you weren't partying or relaxing. Wine in drinking establishments was priced by the sextarius (a unit of measurement equal to about 1.15 pints), presumably already watered down. A sextarius of watered-down wine would have an alcohol content equivalent to about one modern glass of wine, enough to get a very slight buzz while keeping you hydrated. Drinking undiluted wine when you weren't in the appropriate setting was considered barbaric and public drunkenness was embarrassing.
As Romans bought so much of their food, you might be wondering how much they paid. The usual money that citizens would deal with was the silver denarius, which was divided into 16 bronze or copper asses. A typical wage in Pompeii in 79 AD was 1 denarius per day. Surviving records from Pompeii (such as menus written on the walls of tabernae and popinae) indicate prices of 1 to 5 asses for wine depending on quality, 1 as for a Roman pound of bread (about 0.73 American pounds), 2 asses for a sausage, and 4 asses for a meat cutlet. It would be perfectly possible for all but the poorest Romans in a city to survive on purchased food.
The upper class got to engage in all the good stuff, as they had their own kitchens and staff. Apicius is a Roman cookbook compiled in the 1st century AD and provides an excellent look at cooking methods and ingredient combinations. You had ostrich stew with tons of herbs, spices, and vinegar. You had roast venison marinated in olive oil, raisins, and spices. You had vegetable purees placed into molds and cooled. The sky was the limit and decadence was key.