Period cooking styles vary from region to region and were, for the most part, dictated by locally available ingredients.
Making period foods doesn't have to be hard. Many ingredients can be found at your local supermarket.
There are certain things that are not period foods, or were only known in the Old World in very late period, such as potatoes (which will come as a surprise to some), tomatoes, capsicums (bell pepper, paprika, chili, etc.), common beans, and chocolate.