If you want the essentials, you must include Shakespeare, Chekhov, Ibsen, Brecht, and Beckett. These are the real giants of dramatic literature.
For more modern stuff, I would suggest:
John Guare: "The House of Blue Leaves" or "Six Degrees of Seperation"
Caryl Churchill" "Top Girls" or "Cloud 9"
Tony Kushner: both parts of "Angels in America"
Paula Vogel: "How I Learned to Drive"
David Lindsay-Abare: "Fuddy Meers"
Suzan-Lori Parks: "Topdog/Underdog"
Tom Stoppard: "Arcadia"
anything by CHARLES LUDLAM
All of these might be a bit more difficult to read than Arthur Miller or Neil Simon, but each is BRILLIANT in its own way
"Inside every actor there is a Tiger, a Pig, an Ass, and a Nightingale. You never know which one is going to show up."
-John Michael Higgins in FOR YOUR CONSIDERATION