Classic Books That Are Actually Engaging And Deep

Okay so like many Americans who were educated by the public school system I "read" many classic books such as Frankenstein, Catcher in the Rye, The Great Gatsby, 1984, etc. but I never really got to engage with the text in a way that would allow me to enjoy them and remember the details and themes and plot. I used to love reading as a little kid but school killed that for me (I know, I know, woe is me). Anyway, now I would like to get back into reading and I thought the classics would be a good place to start, after all they are considered to be classic for a reason. I just want to read something that isn't too dry of complex and wordy but still deep and thought-provoking, something that will make me think and touch my soul and really leave an impact.

Tldr: I want a classic book that is deep and thought-provoking