The game so nice I bought it thrice, on three different platforms, with a sequel and a spinoff to boot.

Edit: This game is probably one of my favorite games that I've played in recent years. A friend introduced me to the series years ago and now having played through the game multiple times on PSP and Vita I developed a strong liking to the characters and the story that was developing over multiple games. That being said this games story can be slightly predictable and can sometimes fall into obvious mystery clichés that could deter some from continuing onward with your school life. I urge you to stick with it as this game gets deeper as the story goes on and does a few original things that I haven't seen done in other mystery style games or books. The characters are the driving force of this game though and they all have interesting quirks to go along with them. Most players will probably find themselves liking some characters and disliking some others for varying reasons although I believe that each character is extremely well written and have their own unique characteristics that make the interactions between them fun.
Next we have the gameplay which revolves around three distinct sections. Free time allows you to interact with characters and give them gifts much like in a dating sim. Each time you interact with them during this period and give them a gift that they like, they will tell you more about themselves. If you do this enough with any one character you get a skill to help you during the class trials. Next comes the investigation mode in whioch you search the school for clues in order to solve the mystery of whodunit and piece together the mystery of the school and its inhabitants. Finally we have the class trials in which you do several puzzles that lead to the eventual solution to the case. Most of the puzzles are fairly simple so you may want to play on a harder difficulty from the beginning in order to get a more challenging experience although it does get a bit more challenging in the later trials.
TLDR: I would highly recommend this game but be sure to not have it spoiled for you before you play it and be ready for a healthy dose of reading.