The first game that you should play is Danganronpa: Trigger Happy Havoc which came out worldwide in 2014 for the Playstation Vita. The second is Danganronpa 2: Goodbye Despair, which also became available in the same year and on the same gaming platform. The third one is Danganronpa V3: Killing Harmony, which was released in 2017 for the Playstation 4 and Playstation Vita. For the watching order of the anime, you should start with Danganronpa: The Animation, the adaptation of the first game. Its sequel is Danganronpa 3: The End of Hope's Peak High School, which isn't an adaptation of any game and serves as the ending to the protagonists' storylines in the first and second Danganronpa games.