Your Latin teacher was a good teacher. Praenomen (Gaius) is what we would call our first name. To understand Roman names you must understand the Praenomen.
My favorite was the loser Commodus; Lucius Aelius Aurelius Commodus Augustus Herculeus Romanus Exsuperatorius Amazonius Invictus Felix Pius
The Jesuits ha an excellent four year plan. 9th grade was grammar, declensions, conjugations, sentence formation and structure, and vocabulary. 10th grade was Caesar. He wrote in a strict grammatical style. So he came easily. 10th was Cicero’s First Oration . Written for the ear as much as the eye. Using stylistic language and metaphor. Required deeper reading and reader understanding. Finally there was Vergil and The Aeneid. Combining the styles exemplified by Caesar and Cicero and adding the intricacies of epic poetry. It taught us more than Latin. It was the basis for our studies. Acquire skills and knowledge and use them to gradually encounter, overcome, and understand more intricate objectives.