What role if any did the de' Medici family play in Italian Cruisine and the implementation of fine Italian foods?
The de' Medici family is inseparably bound to fine Italian cuisine. In 1439, the Medici's hosted an ecumenical banquet between the Catholic and the Orthodox faction of the then current religious dispute. It was at the banquet that the Medici's first stunned people from all across Europe with the excellence of Florentine wines and food preparation. Then in the late 1460s, Lorenzo il Magnifico de' Medici took control of the government of Florence and made much of his philosophy claiming that the central quest of humanity is the search for pleasure. Lorenzo encouraged the best in all arts, including the art of cooking.
In 1492 Lorenzo died and the New World was discovered, which meant many new and fabulous foods were brought back to Europe in general and Florence in particular, including the bean. Alessandro de' Medici took over the throne of Florence after Lorenzo and he introduced the Renaissance cuisine that featured fully feathered pheasants and whole animals cooked. These creations were in reality never really eaten, merely paraded and displayed as the ostentation of wealth.
As a final note, Caterina de' Medici married Henry II, King of France, and took her Florentine chefs with her in her entourage to France. It is in this way that Florentine cooking reached out and influenced French cooking, eventually raising it to the premier cuisine in the world. For example, the famous French dish Duck a l'Orange began as duck in orange sauce, an original Florentine dish.
[For more information, see The History of Tuscany and Florentine Cookery, Magici Sapori, tuscan and Italian Cookery School.]