I check out these forums occasionally but don't post. I go to St Andrews and wanted to respond to your query. I went to a well-respected private high school in the US, as it seems you do, and I was able to forge very strong relationships with my teachers. At St Andrews it is not the same at all. Below are my experiences; people on this forum might disagree with me, but it might help to know my perceptions. I don't take classics, but I take Modern History and English, and will comment on those.
All the courses that I have taken (Int. Relations, Mod. History, English, etc) are lecture based. I doubt classics would be. In my opinion focusing on learning through lectures is completely inappropriate, especially for literature based classes, but that's another issue.
Lectures are 3 times per week and there is a one hour tutorial, usually with between 7-15 people in it. My lectures are usually about 200-300 people. In the six modules, or classes in the U.S., (3 per semester) I've taken or am participating in, so far, the lecturers have all been professors, I think, while half of my tutorials have been led by phD students). However, lecturers switch off every week or two, so you won't really establish a connection with any of them. Additionally, one hour a week with your tutor won't really be enough to establish much of a connection. Here, many teachers don't have office hours, they have AN office hour. My experience has been that they want to be minimally involved with their students. I am quite good at reaching out to my teachers and had strong relationships with them in high school, but it is definitely not the same here. You will find much stronger student-faculty relationship in a U.S. college or university than you will here. In fact, it is one of the reasons I am transferring back to the U.S.
Personally, I have been extremely disappointed with the teaching. As I am sure you know, as a student at a small, US private high school, learning through discussion is much more productive and interesting than being lectured at. If you enjoyed your high school experience and want something similar in terms of teaching style or community, I can't recommend coming here.
If you want to talk about this more, feel free to respond to my post or send me a message.