My ostensible purpose for playing both the original and Secrets Remastered was to advise players of the original whether playing the newer version is worthwhile. By itself, Secrets Remastered is a good, though unexceptional game. However, I particularly enjoyed playing it in conjunction with (and comparing it to) the original version. If you own the original and are the least bit curious about trends in the design of these games, play the two versions together. (It's too bad the original isn't included on the Secrets Remastered DVD to make it easier to compare them.)
Another reason I particularly enjoyed Secrets Remastered was its many references to previous Nancy Drew games -- in library books, in the jukebox music, etc. All of these allusions contribute to the gamer's enjoyment. But they would be unrecognizable to someone playing this -- the first game -- as an introduction to the series.
So if you're a newcomer to the Nancy Drew games, I wouldn't recommend starting with this one. Since the plot in each game is self-contained, you should pick a game that has a theme or a location that happens to intrigue you, and start with that one. If you want lots of puzzles, start with a game like Last Train to Blue Moon Canyon. If you'd like to see backstabbing intrigue among students in fancy academic surroundings, try Warnings at Waverly Academy. If you'd like exotic environments, try The Phantom of Venice, or if you'd like to be horrified while snooping around, give Legend of the Crystal Skull a try.
Once you've played other Nancy Drew games and would enjoy all the references and allusions in this one, Secrets Can Kill Remastered is worth your while.