Another factor in Tom Stoppard success--or at least a big part of his reputation from the beginning--was that he gave good interview. There are filmed or videoed examples on youtube, though most are recent, but the influential and substantive interviews were for print. The University of Michigan Press collected about 40 of them from 1967 to 1993 (though some are quite short) in Tom Stoppard in Conversation. This volume includes 3 interviews by Mel Gussow of the New York Times. Gussow published a separate book, Conversations with Tom Stoppard (Limelight Editions, 1995) that includes four more, plus Gussow's introductions and afterword. Gussow was always the Times second string critic, and really prospered in that position. Without the pressure of the Times lead reviews, he could pursue enthusiasms and delve in depth. He put together similar volumes of conversations with Harold Pinter, and with (and about) Samuel Beckett. I consider his career exemplary. (Apparently this book is out of print now--I see on Amazon it's alarmingly expensive.)
There's a good biography: Tom Stoppard, A Life by Ira Nadel (Palgrave/Macmillan, 2002.) The biographical chat at the beginning of this piece is based largely on this book.