Here is my advice; when I go on a first date with a girl, I do all the usual stuff; I am very polite, hold doors, try to get to know her a bit, etc.
But then, once you are both getting settled in and relaxed, do something that is just entirely, crazily, stupidly "YOU."
We all have a lot of weird kinks and quirks, that we might be afraid of showing a GIRL for the first time.
Just DO one of those things, or tell her about it, or something. One my first date with my current girlfriend, I told her this.
"Ya know, I know it is really weird. But I really like cats. I call 'em kittens, mow-mows, purr-boxes. And what is even wierder, is a habit I picked up from my mom. I really love it when a cats ears are cold. When they are cold, I really like to play with them. And I even like to bite them. Not like hard with my teeth, but I just kind of 'gum' them with my lips. Can you believe that?"
If she is cool, she will think its is funny or goofy and probably laugh and tell you some other off the wall habit that SHE has. After a conversation like that, you can REALLY relax and enjoy yourself.