The amount and kind of graffiti at Pompeii and Herculaneum, two unimportant towns, suggests that a lot of people were literate. But it’s still hard to quantify.
Well the lower classes couldn read signs. Graffiti was pretty common at Pompeii. It would depend on their job. Labourers wouldn’t have much use for literacy. Slaves would’ve been illiterate except for the ones working as scribes or tutors. Obviously men were more likely than women to read and write. Female literacy was limited except for the upper classes. Boys may have gone to school if their parents could afford it, but girls were taught matronly things by their mothers at home.
So what about the Roman military? Obviously Legatus Legionis would know how to write but about lower ranks, Centurians? Did the romans use written military reports?
The many letters found at Vindolanda on Hadrian’s wall would certainly suggest that a high level of literacy.
I dimmly remember something from Vegetius to the effect that literacy was a requirement for a Roman recruit - although that does seem rather unlikely.
Of course, ordinary Romans did not speak or write Classical Latin in that manner or Caesar etc. They spoke and wrote Vulgar Latin. It seems that Classical Latin has always been formally taught.