Let's say I live in Herculaneum. I've been given the best education, but what were they educating me in? I'm assuming math is a given, but what historians have I read? Who are popular scientific writers? I'm contemporaries with Pliny the Elder, but is his writing popular enough while he's alive for me to know? What philosophers are commonly read? Is religion considered a topic for intellectuals, or do they see it as superstitious?
Hey! So if you’re a man in the upper classes (equites or senators), your entire education is designed for one thing: to boost your political career. As a young boy, you learned Latin and Greek, history (Herodotus, Thucydides, Xenophon), geography (Strabo) and some basic mathematics (but less than you might think - you’ll have stewards and other servants to run your estate for you). When you’re a young man, you might go to Athens to study philosophy for a few years (Julius Caesar did, along with many others). To be civilized, you’d be expected to know large amounts of the Iliad and Odyssey, as well as other Greek literature.
But your biggest subject is going to be rhetoric. You’re going to be visiting the Roman forum to hear court cases being argued. You’ll be expected to argue in court and in the Senate House one day. You’ll study orators like Cicero, or maybe the fashionable “Asiatic” style of oratory popular in the Near Eastern Greek cities. Your teacher will set you debates on famous historical or literary, and you’ll have to argue both sides convincingly.
You’re also doing military service and learning how to ride, hunt, etc. One day you may be a governor of a province, and you’ll have administrators working for you but you’ll still need some knowledge.
If you’re an elite woman, you’re less likely to be literate, but plenty of women were. You’ve had a similar education in your early years, but with more emphasis on managing a household. You wouldn’t have the secondary education in rhetoric.
In terms of religion, you’re expected to participate in public ceremonies, but your beliefs could vary. Maybe you’ve read Epicurus, maybe you’re more of a Stoic or a Cynic, or maybe you’re interested in the fashionable eastern religions of Isis or Cybele. Lots of options.