Hmmm I think a lot of this depends on the class itself. Is this a general education English class? Is this a literature class? I know there are classes on specific kinds of literature, like American classics, or indigenous literature, etc. Is this a history class? A Hellenic Classics course? What books I'd choose, the purpose of those books, as well as the reasoning behind what to pick would depend on that.
But, I think you mean for a general literature English class, to teach the students about whatever point or literary achievements are emphasized in the books themselves, not necessarily following a theme.
Gosh I need to read more classics for sure, I love them and I think some of the highly anticipated ones on my TBR would be in my 4 choices if I'd have already read them.
Let's see . . .
Firstly the Great Gatsby, by F. Scoot Fitzgerald. This is one of my favorite works based on the theme of 'the American dream' which is a big focus in the English classes here, as it pertains a lot to our history. The Great Gatsby carries across the theme better than some of the other works I've read on the same theme, and is easier to relate to our current society.
A Raisin in the Sun. This is another 'American Dream' work, but I think it's important to include as it shows another side of things. If the Great Gatsby is about the American dream (and it's fails, as books on it most often showcase) for rich, white men, then A Raisin in the Sun will show us the American dream from the perspective of a minority. I think this play is really well written, and it was a great window into black culture and experiences during the 1960's.
I would also include some Shakespeare, maybe Macbeth, which is a personal favorite. A Midsummer's Night Dream is great for classes however, because the humor can help keep students more engaged and it feels less dry if you aren't already partial to the court politics of Macbeth (me lol). While perhaps overdone, Shakespeare is really important for understanding other works, and the English language on a deeper level. I think Shakespeare depends entirely on how it is taught, though. I was lucky enough to have a teacher that made it fun, took the time to explain phrases, and historical context, etc. A teacher can make or break Shakespeare for students, so if I were to teach it, my main goal would be to make it as approachable as possible.
I would also want to do The Outsiders by S.E. Hinton. I loved this book in middle school, and it has really great messages for young people that I think college students would appreciate. This is another great book for American history and culture in the last century, and the fact that the author was just 15 when she wrote it can be very inspiring to young people pursuing writing.
I'm not sure if those are the best picks, but they're the ones that first came to mind. Like I said, it's difficult to pick things without a theme, and so I feel like Shakespeare is a bit of an odd one out on this list. Either way, I think these books are important. (Runner up mentions that I also think are good choices: The Hobbit, The Book Thief, To Kill a Mockingbird, Pride and Prejudice).
As for your questions, there really great discussion points and I have a lot of thoughts and opinions I'd love to share. That said, I'm having a hard time wording things clearly and eloquently today, so I think I'll jump back in at some other time. I've been trying to write and rewrite my answers for too long lol .