okay, no disrespect to Neil or the nyt, but i think THE place to start is The Graveyard Book. Sandman, American Gods, and Neverwhere are some of my favorite stories, but they're also pretty long and meandering at times, whereas The Graveyard Book feels like a distillation of some of Neil's best ideas and themes into a tight package that's also a chill read because it's written for all ages. it's one of those rare books like The Hobbit or The Giver that really transcends age-range and has something of value for everyone. it's also the only book to win both the Newbery Award for children's fiction *and* the Hugo Award for Sci-fi/Fantasy literature, which honestly shows you just how universal of a story it is.
Neil Gaiman is my favorite author, and The Graveyard Book is always the book i recommend because it's a short, accessible read that is representative of his style and leaves you both wanting more and primed to jump into his longer works. so yeah, go read it!