Examine your main elements and decide which one is most responsible for driving your plot forward. Every writer may think that the main elements--plot, character, setting--are all equally important, but sometimes one part outshines the others. In the story "Midnight in the Garden of Good and Evil," the setting of Savannah, Georgia, and the town's mood are very prominent versus the whodunit murder plot. Find your centerpiece and commit to that as the story opening's main element.
Make the tone of the opening match the dominating tone of the story. Opening "Schindler's List" with a comedy bit wouldn't serve the story well. The important part of the opening is making sure the reader starts off on the right foot and mind-set to best capture the story's theme. By staying consistent with the tone from the start, you have a better chance of making the story memorable.
Be specific in description of the characters, setting or plot element. If the story is character-driven, a vague description will only make a main character just like anyone else in any other story. Saying the story starts in New York (a very large city) versus describing a specific portion of New York (the dingy streets of south Chinatown) can make a world of difference.
Focus on establishing the beginnings of your story within one or two paragraphs, regardless of what the centerpiece will be. It shouldn't take long for the reader to figure out that you are setting up a big plot. "Gone With the Wind" was a good story about the Civil War, but the movie script beginning clearly outlines that Scarlett is the focus of the story with her dismissal of the war and how it "spoils the fun." This opening perfectly describes the attitude she has throughout the story, which ultimately leads her to making huge mistakes that drive the plot and drama throughout.