His best book is "The Old Man and the Sea", but although stylistically it's wonderful, it's probably not the best place to start.
Many people consider "For Whom the Bell Tolls" to be his best, but that's completely false. Anyone who says it's a great book is deluded, it's downright awful.
"A Farewell to Arms" is terrific, but it's a bit of a downer and it can get quite slow here and there.
"To Have and Have Not" is widely considered to be his weakest novel. I don't agree with that assessment. If I remember correctly it was the first Hemingway novel I read. It's not going to knock your socks off, but it's a solid book.
As cliché as it is, I honestly think that "The Sun Also Rises" would be the best place to start. It's well-written, the characters are vivid and the setting is almost a character itself.
Of course, you could opt to go with a collection of his short stories, many of which are fantastic, but if you'd prefer to go with a novel, make it "The Sun Also Rises."