Quoting Supafly★:" Lol you just described me and my bestie to a T. I'm the rap-loving girly girl and she's the grunge-punk tomboy. Neither of us are neat freaks though. I'm slightly neater than her, hah. "
Lol thats funny.
I think you dont need much or anything in common to have any kind of relationship to work out. Sure it may help when first buliding a relationship and all, but totally not a given.
I usually lead with a compliment like "I love your shirt! Where did you get it?" Or "your hair looks great! Do you use a special shampoo or are you just one of those lucky girls?" That usually leads the conversation to some common ground, favorite places to shop, favorite beauty products, stuff like that.