I don't know whether any of this might help you, Hannah:
Barrie's first book was indeed Better Dead, and he paid to have it published. His second book was Auld Licht Idylls, a collection of his articles which had appeared in the St James's Gazette, and its sequels were A Window in Thrums, a collection of stories about his childhood Kirriemuir and its people, and the novel The Little Minister. This latter book was certainly a big success throughout the British Empire, so perhaps it could be classed as Barrie's first major successful novel.
Moving to his plays, Ibsen's Ghost, a one act play, was the first which he wrote on his own, and it seems to have been a minor success. His second, Walker, London, was far more successful, and, at Barrie's insistence, it starred Mary Ansell (his future wife). Perhaps this play could be classed as his first successful play?
I gleaned all this from Andrew's excellent book. If you haven't read it, then I urge you to buy a copy. See it on this Amazon.co.uk link
http://www.amazon.co.uk/exec/obidos/ASIN/0300098227/qid=1110881994/sr=1-5/ref=sr_1_11_5/026-3838939-6951655