I had spent the better part of my sophomore year beginning ancient Greek and, realizing that I'd come to the Classics late in my college career, determined that the only thing to do was to teach myself Latin over the course of the summer.
Does the Classics mean the department of Classics?
What does late in my college career mean?
I need native speakers' help.
I speak American English. A British speaker can add to this.
It looks like you're quoting a text that is more than twenty years old (or maybe British, I don't know). Today, most Americans would use a small c in that sentence. The classics are the old literature that is the foundation of high culture. People study ancient Greek and Roman culture to understand Western culture today.
In this sentence, late in is an idiom that means near the end of.
Career here means experience.