Cups and mugs for camping are mainly made of melamine and less often of other materials such as polycarbonate or metal. The mugs can be bought so that they match each other and match your dinnerware set.
The mugs can also come in sets of 4 different colours, which could be practicle for when you want to minimise the washing up. That way you can delegate a colour to each family member and use it throughout the whole day.
Most melamine mugs are dishwasher safe.