A.R. Gurney's new play The Grand Manner, which begins previews June 2 at Lincoln Center's Mitzi Newhouse Theater, is inspired by the playwright's real-life encounter with the legendary actress Katharine Cornell, which took place after a 1948 performance of Antony and Cleopatra. It's a heady challenge for any actress, but it's one that three-time Tony Award nominee Kate Burton is ready to tackle.

"I think Cornell could diva it up with the best of them, but she was known for being pretty down- to-earth and for having an incredible, robust sensuality," says Burton. "Gurney says his encounter with her changed his life and got him started on his path. The theme of the play is what is art -- and how does it change? When you have a great actor like Katherine Cornell, what happens when her grand manner goes out of style? Can she transition into a new era? It's a very profound experience for those of us who are in the theater."

Burton literally grew up in the theater as the daughter of the great actor Richard Burton. And she learned the plus and minuses of fame early on, by spending summers with him and then stepmother Elizabeth Taylor or regularly bumping into celebrities at Arthur's, the popular New York disco owned by Kate's mother, Sybil Christopher.

And once Burton decided she was going to be an actress, she chose the Yale School of Drama over the more classically-inclined London's Central School of Speech and Drama. "I had an American accent and I also thought being an American actress would separate me from Dad," she says, laughing in hindsight at that impossibility.

But as Burton talks about her life -- which includes her 25-year marriage to director Michael Ritchie -- in her warm and down-to-earth manner, one realizes just how well she has avoided the pitfalls of living up to the grand manner. "I know from growing up in the spotlight, as it were, that the most important thing is your family," she says. "My mother is bustling around running her Bay Street Theater in Sag Harbor, I'm married to an incredible fellow, and we have two great kids. I'm very lucky."

Burton made her Broadway debut as Daphne Stillington in George C. Scott's celebrated production of Noel Coward's Present Laughter at Circle in the Square in 1982; and later that year she played the title role in Eva La Gallienne's production of Alice in Wonderland. But it wasn't until 2001 that Burton truly became the toast of Broadway when she played the lead in Nicholas Martin's production of Ibsen's Hedda Gabler.

Her preparation for handling that iconic role, she says, came from taking over from Kate Nelligan in the Broadway production of Wendy Wasserstein's An American Daughter and then stepping into the Broadway production of Martin McDonagh's The Beauty Queen of Leenane, in which she later toured Ireland and England. "Beauty Queen is the weirdest, strangest, and most perfect play to do before Hedda Gabler, because there are so many similar issues for Maureen and Hedda. I had played leading ladies before but couldn't really hook into them. After An American Daughter and Beauty Queen, I had all the ballast."

Just three months after Hedda Gabler finished its limited run, she was back on the Main Stem as Mrs. Kendall in the revival of The Elephant Man -- and ended up as a two-time Tony Award nominee in the same season. "I actually feel so blessed that I wasn't some 23-year-old doe-eyed actress when I could handle it," Burton remarks. "It's pretty swell, I've got to say. I wish it meant more -- and yet it's probably fitting that it is what it is. It's a wonderful laurel and the next day you are back pounding the pavements."

In fact, she has had a chance to share that wisdom with current cast member Bobby Steggert (who plays the young Gurney), who just received his first Tony nomination for his work in the revival of Ragtime. "I said to him, 'it's too bad you are rehearsing because, frankly, you could exhaust yourself with the luncheons and cocktail parties,'" she notes. "He's such an extraordinary young actor. We are learning from him and he is learning from us -- it's pretty incredible."

Still, there's another young actor that Burton really wants to work with again: her son Morgan Ritchie, who co-starred opposite her in The Corn is Green at the Williamstown Theatre Festival in 2007 and then again in 2009 at the Huntington Theater in Boston. "He's a natural talent," Burton enthuses. "I see my father in him; he's bigger than my dad; but he has my dad's physicality and a lot of his facial features."

She's actually saving one of her dream roles, Arkadina in The Seagull, so she can play it opposite her son, "He really wants to play Treplev," she says. "It ultimately becomes an asset to be part of a theatrical family if indeed you're good at what you do. I was lucky enough to be able to grow and mature in a natural way as an actress."