The best line... is not a line but a point. hahaha Im just messing with you but I do got a point as in - you make a point about something that is contextual to a situation.
bla bla da neee wink wink jk aside - I hear its a good tip to ask her for a favor first like "can you pass me the xy" or whatever the fuck is situationally adequate. When she does that you can open with something.
"I like your shirt" when it comes from nowhere sounds a bit less suave than "do you know the time, my sumaho died.." time is now or never sailor "Oh bdw nice shirt, I like flower patterns".
From my experience and if anything I have experience approaching girls.
Have a nice smile, look your best, establish a safe atmosphere, be casual and relaxed and fun. The mental state you are in speaks louder than your words.
Id first try to establish a rapport via body language, like, be in observable distance from the girl, try to see if she's looking, exchange few looks or smiles if possible. Maybe even a wink if you feel dandy.
Then approach and comment on something about her that captured your attention. And be genuinely interested in her day, what is she doing, but not in FBI type of way, but more like rub the lamp until the spirit comes out by itself. Kinda nudge conversation into being.
Keep things fun and light. You could ask her for a coffee then and there, its not impossible. Even if there is more of them. Think in terms of making friends.
My rule of thumb is - the goal is not the number, or the kiss, or the hug. The goal is to GET TO KNOW the person. Dont forget the forest for sake of trees. See the big picture. You want an LTR so you do want to become intimate, intimacy is getting to know the person. This is not seduction in terms of "best lines" or "what to say to get her to do xyz". Its being socially adept while rising levels of intimacy.
So be interested into her, in a respectuful non intrusive way, be fun and show her you are a man after all in some comfortable way, more and more as time goes - if she is responding well, if not, then get back to establishing more rapport. But the point is - if you really want LTR - you will know which girl vibes with you and which one doesnt.
Another rule - if it feels like you are fighting a one man battle, usually its time to back off. A girl who is feeling you will be on your side very quickly and help you even if you fumble, to get to know her better.
Also dont ever get butt hurt over anything, just water of ducks back. Respect yourself but dont be emotional and childish.
Women sometimes are just surprised by being approached, or inexperienced or lack confidence, and sometimes they lose the opportunity because they may appear cold but they are just shy and surprised.
You cannot be her clown and do everything but dont always assume worse just because she seems lagging in a way. An exchanged contact and "what u up to?" here and there can lead to something over time.
And biggest fucking thing ever, talking especially to myself - first throw a wide net, then harpoon. Which means - arrange many dates, meet many women, think in terms of abundance build abundance mindset in yourself and then when one bites properly you can let others go. Dont make the error of finding a quirky girl u like and then becoming all over her and giving her too many chances to learn you lost all self respect since u met her.
I used to feel it was immoral from me to approach girls while I was "working the girl I liked into being mine" but I lost a lot of opportunities that way and only acted too desperate.
Just keep your options plenty, they do it too. And its a bigger compliment to choose one from many you have prospects with, than one because thats the only one.