> a ceramic mug

Not so fast! A ceramic mug takes a huge amount of energy to produce, so unless you reuse it many times, it won't break even:

https://terngoods.com/blogs/learn/cups-single-use-disposable...

Keep in mind that even a ceramic mug eventually becomes trash - with a far higher mass than paper/plastic cups.

Then of course there's the environmental impact of washing the cup, but I don't have any data on that.

You say clearly, but the full lifetime calculation is difficult.

I have no idea how the clay is obtained, transported to the mug factory, how it's turned into mugs, how the mugs are transported to shops and then to cafés and homes. I don't know how to include the detergent used to wash them, or the dishwasher. I guess we need to include the hot water, but how much of the plumbing do we include?

I also don't know any of this for the paper/plastic cups.

True, can't pretend to know either. Reuse, in as many of those areas you mentioned as possible, seems like the key way to optimise.

Using second-hand ceramic or glass is maybe a good thing to think about. No signalling of demand to a manufacturer, maximising return on the initial co2 cost... Perhaps not viable in every situation.