Mark Twain is easily the greatest writer the US has ever produced. Read just about anything he writes and you will be doing yourself a favour. My personal favourites are Connecticut Yankee, Puddin'head Wilson, Tom Sawyer, and of course Huck Finn. In that order.
Death In Venice is about a homosexuals infatuation with a teen-aged boy. I believe it is reputed to have merit. I couldn't find it. That is not to say it isn't there, it just wasn't there for me. Nabokov's Lolita on the other hand is just about the funniest book ever.
I find most James Joyce incomprehensible...and I've read everything he has written. Maybe I am missing the symbolism.
One Flew Over The Cuckoo's Nest? Absolutely. Ken Kesey was part of the whole beat generation thing with jack kerouac, and this book has some of the same feel. The main character is as wild and non-conformist as they come.
Dorian Gray? Read it years ago and it made no impression on me. If it had been in any way memorable I would comment, but I can't. To each their own though. I have also read James, Kipling and Flaubert. I don't have especially glowing recommendations for any of them. They are obviously highly regarded writers, they just didn't affect me in any way. If you want classics I'd recommend Dostoyevsky, Hugo, Dickens, Orwell, Homer, Cervantes