I have no problems with a girl comming over and talking to me, I might be attracted to her aswell or I might not, I might become attracted to her personality if her looks wouldn't be too "amazing".
I don't know her yet, so first thing that'll be "judged" is appearance and how she "carries" herself.
Personally.. I like "different" people.So not the usual... hey how are you, what do you do, where do you work/go to school, what direction do you follow if your in school, what do you do for fun etc.
I like people who can "read" the situation, comment on it and then just start about something related or even completely different that isn't related to who i/they are as a person. Its "abnormal" or at the very least uncommon and thus more enjoyable.. at least that's what I think ;)
an example of a few days ago;
I was walking to the trainstation as I had just finished work(i'm a lifecoach) but I was still thinking about a few things I should do/do when I get home and this girl who walked by simply asked me "why do you have such a puzzled face?" and from there it just came naturally, we talked about my weekend, told the story of why I had that puzzled face and then eventually we got to me enjoying to travel, her study on travel & culture and we just talked about whatever came to mind.
I had fun and I'll see her again next week for drinks =)
The more you try to force a conversation or "stick to whatever I'd say now" the worse it'll go as the less natural it'll seem and the more it'll seem like you planned it all in advance, the reason I stopped to talk(and figured I could take the next train) is because she read the situation and commented on it and just started talking about whatever I threw at her, it was fun and it was absolutely random which made it interesting.