Like TimovieMan said, it all depends on what kind of games you like.
Hotel Dusk - Excellent Noir adventure, probably closest to point & click from that list
Layton - if you like lots of puzzles
Phoenix Wright - If you like dialogue driven stories. Very funny.
My answer? Why choose one, get them all
I've got all three and love them all.
If you had to pick one first, and are equally open to any one, I'd pick Phoenix Wright. Its funny, the story is great and the gameplay mechanic is different from anything else you've played before.
Also, I'd consider what thejobloshow said about Ghost trick and I'll add 999, both of which are newer games that I havent played, but get rave reviews by everyone who has played them.
