I'd guess a quick-to-make traditional variety like most "squeaky" cheese - softer, often crumbly and sticky, probably not good for books. A hard cheese probably wouldn't produce as many crumbs or be damaging if it did.
I was thinking that Medieval preservation was basically "add more salt until it doesn't rot," so everything was way saltier. Plus they didn't have the cheese-making techniques we have now. No precise temperature control, aging caves, or quality standards so just "milk that won't kill you, aged until hard."
When I was in cooking school, it was assumed we would not have the time or equipment to constantly be monitoring temps with a thermometer so we had techniques for determining fairly precisely the temp of things.
Poaching liquid was evaluated based on the quantity and rate of bubbles rising from the bottom of the pan.
Milk was scalded (e.g. for bechemel) when the milk foamed but was shut off before it boiled over.
A knife inserted in a steak, chop, or roast could be tested for temp against your lower lip or wrist (yes, yes, hygiene and so forth).
The techniques you are talking about all came about because of all understanding of food that led to science asking "why does cheese happen the way it does". The precise techniques leading to a sharp, hard cheese or a soft, fresh cheese were well understood long before instant read thermometers.
Hard cheeses were a preservation choice, not something they had to do. Charlemagne is recorded to have enjoyed cheeses similar to modern brie, for example.
Medieval Europeans also liked pickling and smoking as preservation methods, for what it's worth.
Poaching liquid was evaluated based on the quantity and rate of bubbles rising from the bottom of the pan.
Milk was scalded (e.g. for bechemel) when the milk foamed but was shut off before it boiled over.
A knife inserted in a steak, chop, or roast could be tested for temp against your lower lip or wrist (yes, yes, hygiene and so forth).
The techniques you are talking about all came about because of all understanding of food that led to science asking "why does cheese happen the way it does". The precise techniques leading to a sharp, hard cheese or a soft, fresh cheese were well understood long before instant read thermometers.
Fresh cheeses too, like cottage, ricotta, and farmers cheese, which wouldn't have been too salty.
Medieval Europeans also liked pickling and smoking as preservation methods, for what it's worth.