how important was education and family to the roman republic in the 1st century BC?

Answer 1

There are three answers. First, for the Patrician class, it was a point of family pride to perpetuate the ability of a family's children to continue their place of importance and wealth (it was very expensive to be a patrician, there were social obligations, look up patron). Second, the Plebian class usually couldn't afford it, but there was the equivalent of an apprenticeship to teach trades. Articulate, literate, and talented plebes who had a good patron could get support for a better lifestyle--but that came at a price, kowtowing to the patron's whims and wishes. Third, there were the slaves, a very sizable share of roman population. The educated and cultured slaves were often impressed to be tutors, teaching the Patrician children in private lessons. Those who weren't got the 'grunt' work.

Family was important to Patricians, they had to sustain their place. Family was more marginally valued to the Plebes because their social prospects were considerably more dismall. Male children could learn a craft if they were tradesmen, continue the family business if they were merchants, or keep farming if there is enough land. If there were too many males, well, there was always the army which continually needed footsoldiers (officers and cavalry were Patricians, who else could afford a strong but expendible horse?) for their perpetual wars or subjugation of a wide range of people. But Plebe females, particularly, was a problem. Every woman, whatever the social rank, had to have a male responsible for her. Too many women could easily become too expensive, and a bride with no dowry only got scuzzy husbands, and dads didn't want that. The other factor reminds me of a friend who realized why his father-in-law hated him, "Because I was [having sex] with his daughter." Surplus women, therefore, often had to compete with slave prostitutes. So, surplus baby girls were often "exposed", abandoned to wild animals in the city dump or drowned or strangled. As for slaves, a similar thing takes place--copulation with female slaves makes more slaves, a profitable undertaking.