There's something to be said for learning the "canon" but high school English only does that in a very superficial way under the best of circumstances. There are fairly classic books--at least some of which are admittedly more recent than ye olde public domain--which are pretty readable today. But IMO Henry James, Bronte sisters, Tolstoy, etc. are going to be a pretty tough slog for most modern readers, especially at high school age.