The longest journey is a very good game. Good story, good characters, nice art style (although from a technical point of view the game has aged relatively poorly), good voice acting and an interesting setting. It is one of those must play adventure games, just expect to listen to a lot of dialogue.
Its sequel, Dreamfall, has action scenes and is, by adventure game puritans, not considered a pure adventure game, but don't let that stop you, it is still an excellent game!
Other games worth considering:
Syberia 1 & 2 (needs to be played in order). I found Syberia to be better than TLJ, due to its puzzles. I also loved the art style. There is a collection of the two Syberia games and Amerzone (an earlier game by the same people) called Syberia collection that you should be able to find for about 12€. Amerzone is not nearly as good as Syberia, but it is still worth playing through (it is an incredibly easy and short game, I finished it in just over 2h)
Myst: Not at all like Sanitarium or The longest journey, but I love it (the puzzles are great in the myst series!)
The last express: This one is a bit different from the normal adventure game. Most AGs are strictly linear, offering a single solution in a rather static world, the last express offers multiple solutions in a constantly changing world (people move about on the train, doing what you would expect people to do). One of the finest adventure games of all time.