I really don’t think you can say there is a best way to have a beginning of a script. The genre, itself doesn’t seem to matter, but the _ whole concept_ does matter.
Two of the most effective beginnings for movies that I’ve ever seen are the opening title story in Star Wars episode IV and the psychedelic semi-animated dance sequences at the beginning of the James Bond movies. Those beginnings set the stage for what was to come next.
I’ve seen tons of smaller (non action oriented movies) that have started in all sorts of ways, from a closeup of a silent person’s face, to a long shot of people walking and talking in the distance, to a super close up of some type of object, rather than a person, but you hear dialogue in the background. It just depends upon the whole concept of the screen play as to what will work best with any type of screenplay. Some of the best movies I’ve seen have creatively started from the ending and worked back towards the beginning, and it was only then that the whole concept became clear and made sense.
If you gave the same script to 10 different screen play writers, they would probably all come up with very different ideas of how to start. Some would be boring, some would be average and common, and some would be brilliant. One movie that really touched me had a lot of very common, almost mundane scenes of life and almost no dialogue, that was The Girl with the Pearl Earring. I tend to like those “slice of life” types of movies, and I’ve discovered that most men hate them.
So it depends upon the concept that is being put forth and it partly depends upon the target audience. Same story with a different concept and different target will reap very different results. Imagine if The Sound of Music focused on the War and the brutality of the Nazis rather than on the music. It could still be a very good movie, but very, very different.