you will appreciate the anime more by watching it first. I never really cried during the anime nor the VN, I shed a tear during some of the routes. You will however feel very empty and somewhat depressed during the visual novel, I don't really remember the anime that much. You shouldn't take it too seriously though, much of the plot is forced and is supposed to make you feel bad.
Anime, game(whole), movie (I guess) and then the after story anime when it airs.