That doesn't really help. I mean, I get you're looking for classics, but I don't know how far afield you want to go from the stock stable. If you want to stick to high school and college required reading stuff like you seem to be (I don't mean this derogatorily, as most of those will be great reads, and likely all better experienced at your stage of life anyway), you can easily find more of it than you could read in 10 years without ever asking anybody. But if you want something tailored to your taste or interest, or to narrow down the scope a bit, that's another matter.
Anyway, I'll just throw out some stuff at random:
Kerouac is essential, despite being way, way overrated. Burroughs is more fun (Junkie, Naked Lunch, and maybe The Soft Machine if you want to stretch your legs). I'd highly recommend some Bradbury: Fahrenheit 451 is the go-to essential, but The Illustrated Man is up there (short stories). There's This Side of Paradise and The Great Gatsby for F. Scott Fitzgerald, though there's no reason to neglect Flappers and Philosophers or Tales of the Jazz Age if you like short stories. For Rand, Atlas Shrugged is obviously a big one, but honestly, she's boring as hell unless you've got a lot of patience. I got through AS and The Fountainhead, but they're not exactly what you'd call page-turners. H.G. Wells's The Time Machine. Anything Hemingway. Faulkner's As I Lay Dying, The Sound and the Fury, or Light in August. Steinbeck's The Grapes of Wrath and East of Eden. J.G. Ballard's High-Rise and Crash if you want to get a little more modern. Some might scoff, but I say Stephen King's The Stand should be required reading for anyone looking at classic American literature. Poe's short stories for more definitively classic horror, along with Lovecraft, obviously (Poe only did one novel, of which I'm not a big fan and I'm not sure about its "classic" status, so he and Lovecraft would just be short story collections). Would also highly recommend Arthur Machen's short stories for horror, and definitely Robert W. Chambers's The King in Yellow. Moby Dick for Melville (one of my all-time favorite books, and probably the most quotable book I've ever read).