Most of my knowledge is of British/English history - any generalisations here are about that unless mentioned otherwise. I would recommend looking up medieval recipes for different European countries - food traditions were considerably more local hundreds of years ago than they are now.

It varied a great deal by class: the wealthy ate a large range of meats, including small animals and birds that few in the West would eat today, whilst peasants had far less access to meat. (Remember the prohibitions on poaching in Robin Hood and many other stories?) A lot of peasant food was pottage, a soup with any available suitable ingredients thrown in.

Medieval children apparently had a rather limited diet: http://www.ancient-origins.net/news-history-archaeology/study-reveals-surprising-facts-about-diets-medieval-children-england-005442?nopaging=1

During the early modern period, British yeoman farmers were on average wealthier than their counterparts on the continent, and the British (an obvious influence on American eating habits) were known for eating more meat, hence the term "les rosbifs" which emerged in the C18th.

The railways had a huge impact on diet in Britain, as fresh food was transported about for the first time, and national brands of food arose for the first time. For a lively and more detailed explanation of this, check out episode 3 of the BBC series Full Steam Ahead. As railways became more prevalent elsewhere, the same trends emerged. This is a long paper about the Victorian diet, a key transitional period: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/

Meat had always been associated with wealth and prestige - as people became better off, most of them wanted to eat more of it, and before the health benefits of vegetables became known as vitamins were discovered, vegetables were often regarded as inferior and less healthy.