I know as much as the next gal that classic adventure games aren't for everyone. But if you were thinking of dipping your toe in the genre, Thimbleweed Park is a great place to start - because you're starting at the finish, almost. The game was created by Ron Gilbert and Gary Winnick, who worked on some of the most famous adventure games to come out of Lucasfilm (later LucasArts).
It may be a spiritual successor to games like Maniac Mansion or Day Of The Tentacle, but Thimbleweed Park has a definite X-Files, or even Twin Peaksian vibe. Two FBI agents turn up to investigate a murder. A young woman investigates the dark secrets of her family. Her dead father navigates the afterlife as a sad ghost. A very sweary clown tries to get his life back together.
All the things you look at, pick up, use with your nine-verb menu are rendered in gorgeous pixelart - still somehow very expressive. And while some of the puzzle solutions do get a bit obscure (use teddy on t-rex type of thing) the game added its own version of a tip hotline if you get stuck.
I have a lot of good things to say about point 'n' click adventures, and a lot about this one specifically. If you're not convinced, try the free mini-adventure that came out a couple of weeks ago, and see what you think.