Haha, sorry if I'm chuckling, I just find it sort of funny. How to this,how to that... If you think the girl is cute, just go up to her and talk to her.
You know, girls are so moody that they'll recommend different approachings/initiations everytime you ask. So, if we're gonna be moody about it, you might as well to. Don't you think?
For example, if on one day you wanna talk to her with an opening line like "I'm sorry, this is stupid. I don't even know you, but you keep popping into my mind so I thought I'd come and actually talk to you...", do it. Or if on another, you're very much in an indecisive mood, just be neutralish and say "hi, you up for talking?".
The only disturbing thing is that you guys all make it sound like you want to score a definite hook up. But how do you think you're gonna make best girl mates(with fit friends that you might end up getting on really well with)?
Final analysis (You must all think I'm bipolar):
Do what ever the hell you want, its your life.