You've asked her out and thought dinner and a movie would a good idea. Now you want to know what the best movies for a first time date are.
first of all it depends on what is playing at the time of your date. Go through the listings and make a short list of what you think she may like to see.
Then, the next time you speak with her present her with the list and ask her to make her selection or make her own suggestion as to which movie to see.
The best movies for a first time date would most likely be what they call a "chick flick". I can hear the groaning already, but some silly rom-com would actually be perfect.
Maybe you could get lucky and she is not into those types of movies at all, that's why you need to ask. Never assume, or presume, anything about your date. Her tastes may run completely different from any other woman you dated in the past.
Heck she may even like to watch sports on TV, you will never know until you spend time with her or you open your mouth and ask her.
Usually though, "chick flicks" are the way to go.
I would advise against anything too violent like war movies or alien invasion movies unless they are tear jerkers like "War Horse", or "Titanic" or like "ET" was back in the day. I know I am probably aging myself with that one but you get the idea.
Asking her what types of movies she likes is all about getting to know her. Communication is something that is learned and to do it well you have to keep those lines open at all times.
Not to mention, you nee to listen and remember what she say about the things she likes and the things she doesn't. Not just movies but music and flowers and stores she buys her clothes and shoes.
You need a well rounded knowledge of her and the same goes for her, as well. Do not be shy in telling her the types of movies, music and whatever else you deem appropriate about yourself to her so she can remember those things about you.
It is all about getting to know each other so the relationship can progress steadily.
For the first few dates I would actually steer clear of the big blow 'em up, shoot 'em up kinds of movies. She may like them well enough but they may not be appropriate until you get to know each other better.
Scary movies may be a good choice and then again, they may not be, depends on the movie. You could try one that has a good plot and maybe even one that has a few of those "startle" moments so she jumps into your arms and gets popcorn everywhere.
All in all, the best movies for a first time date are whatever she picks from the available choices at the time.