For me, graphics might be one of the important factors when deciding whether to play an otome game, but I can't say that with complete certainty either. A game with graphics that aren't particularly impressive, like Sangoku Rensenki, can actually make me like it and become more attached to it than a game with beautiful visuals but a story that doesn't appeal to me.
If I said it was the voice actors, I couldn't say that with complete certainty either, because when I choose to play a game mainly because of its voice actors, I usually end up not finishing it. Most of the time, it just doesn't click with me. And what about reviews? Maybe they do play a role. If a game has overwhelmingly negative reviews, I definitely don't want to waste my time playing it. That's probably the one thing I can say for sure. But even if a game has amazing reviews, if I don't get that feeling that it's the one according to my intuition, it'll just sit there in my backlog untouched!
So I guess I'd say it depends entirely on my mood at the time. It's more like, "What game do I feel like picking up today?" For example, if one day I'm in the mood for heavy drama and a serious, emotionally intense story, I'll pick up a game that's known for having a heavy storyline. But if I'm in the mood for something light and easygoing, I'll pick up a game that's known for being funny.
So in the end, I think it's probably my intuition that determines which game I end up playing on any given day.