Grapes of Wrath is a must-read, but for Steinbeck, I prefer East of Eden. Both great though.
I like Hemingway too, The Sun Also Rises or Farewell to Arms would be the places to start there.
I've not read Anna Karenina, but have had it on my bookshelf for years, maybe I'll get to it this summer. I've read The Brothers Karamazov, and my wife wants me to read Crime and Punishment... but I'm thinking one big Russian novel per year is plenty.
Of the ones you've mentioned that you've already read New Dawn, which are your faves? I love Heart of Darkness (you'll have to geek out on Apocalypse Now after finishing it, then check out Hearts of Darkness, about the making of Apocalypse Now), and To Kill A Mockingbird is one of my faves as well...
A couple other recommendations: Ken Kesey: Sometimes a Great Notion... One Flew Over the Cuckoo's Nest is more famous, but SAGN is probably my favorite novel ever.
And, of course, The Great Gatsby is brilliant as well. I think I read that once every couple years or so...
Fun stuff.