That's a good question. If you have never played a Nancy Drew game before, you might want to choose one of the easier games. The older games are not going to have as good a graphical quality as some of the newer ones, but some of the older games are very good. Also, with the newer games, if you play in Amateur mode, there is a built-in hint system, which is nice.
Of the newer Nancy Drews, I would recommend:
Ghost of Thornton Hall
Tomb of the Lost Queen
Of the older Nancy Drews, I really enjoyed:
Ghost Dogs of Moon Lake
Danger on Deception Island
Secret of the Old Clock
Last Train to Blue Moon Canyon
Hopefully some other forum members will put in their recommendations. There really isn't a Nancy Drew game that I haven't enjoyed on some level - I just liked some better than others.
I am also going to move this thread over to Adventure Game Discussions, since these are full-on adventure games.