For me a good story is a must as well. The first game I played was Kana - Little Sister which is still one of my favorites today. The 2nd one I played was Private Nurse. Although I liked the story, there was a few times that I actually skipped some of the H-scenes to get back to the story.
YUME MIRU KUSURI was a great game and also liked the music in it. The main theme was stuck in my head for like a few days. Snow Sakura compared to other bishoujo games I have played seemed kind of average story wise. Haven’t played Raidy yet so can’t comment on it. The Sagara Family was a good game as well. I did like it better than Snow Sakura.
At the moment, my favorite games are probably Fate/Stay Night, Tsukihime, and Clannad. For Clannad, I didn’t mind that it didn’t have H-scenes in it, but I don’t think having them in there would have hurt it either. Once in a while I don’t mind playing a game like Utawarerumono, but for once, I would have preferred if it had voice overs in it. I must of have been spoiled by the anime. Sometimes it feels like after I find out that an anime series was created from a bishoujo game, I want to play it even more. Overall I don’t usually stick with a particular genre of bishoujo game or visual novel. I liked Black Bible as well, but haven’t had the chance to play Discipline yet.