I second the To Kill A Mockingbird, GWTW, and A Brave New World and Jane Austen reccs. I hated 1984 but loved BNW.

Any Shakespeare is good. My personal favorite is MacBeth.

Paradise Lost (Milton) and The Inferno (Dante)

Great Expectations is a good read.

Le Morte d'Arthur
by Sir Thomas Mallory and continuing on that The Once and Future King is excellent.

Continuing with epic poetry Beowulf would be good. The Seamus Heany translation is really accessible.

Books that I typically see in "classics" collections are Dracula, Frankenstein, Tom Sawyer, Huck Finn, Wuthering Heights, etc. This list from the Cincinnati has a bunch on them.