I've actually been working on a book like this! I was frustrated by the lack of information about the evolution of common drinkware throughout history, so I began work on compiling the information myself.

Most of our earliest cups in history were stoneware, albeit not your smooth and shiny porcelain. Fired clay is very easy to work with even on a building scale and the material is extremely cheap in most areas, so it's the obvious choice. The Ancient Egyptians were early pioneers in making glass and faience (a quartz paste ceramic sort of like a cross between glass and stoneware), but the glass was very expensive and completely opaque. Daily drinkers were still ceramic.

The first widespread use of glass drinkware was the Roman Empire. Around the 1st century AD, the Romans discovered glassblowing. What was once an expensive luxury could now be made quickly and cheaply enough for the "middle class" such as it was in Rome to own them (the poorest people still used ceramic, often mass produced now in molds, and metal and ceramic drinkware was still common for everyone). Glasses became a distinctive sign of Roman influence, with the practice of glassblowing spreading where the empire did. Outside the Roman sphere of influence, pottery was the way to go; China famously developed porcelain in many distinct varieties that became valuable trade goods for centuries until the process could be done everywhere with the Industrial Revolution.

The drinkware used has thus long depended on your status, wealth, and location. While glass was cheaper now, it still wasn't as cheap as stoneware or leather. Common mugs in medieval England were actually leather jacks, made of stiffened leather treated on the inside with pitch or beeswax (which was more expensive but didn't taint the drink's taste). Wooden tankards were also used, which got very cheap when they could be made of pieces of wood joined together and sealed watertight. The 18th century onward saw the widespread use of metal tankards and mugs, usually pewter or tin, with the wealthy having silver (often passed down over generations or given as gifts and awards).

As far as the use of ceramic coffee mugs and tea cups, similar coffee mugs have existed for centuries. The basic mug shape can be seen as far back as 10,000 BC, as well as large ceramic tankards from both England and the Ottoman Empire since the 16th to 18th century. Chinese porcelain was an important trade good, as I said, and many attempts were made at replicating it like Turkish fritware in the 15th century. Chinese teacups were custom made for Western orders and mass produced with American flag decoration.

By the 18th century, production of bone china (made of bone ash) became extremely common. With the practice perfected, porcelain could be made anywhere in the world that you opened a factory and was now very cheap. The Chinese monopoly ended and porcelain teacups went from valuable imports to commonplace for all classes. Likewise, mugs in the same shape that had existed for thousands of years could be cheaply made of this insulating material.