There are basically only two ways to embark on writing a screenplay. The first is to come up with an idea – usually a high concept one – and then start plugging characters into that idea. With this approach, often the title alone is enough to understand the entire story: Wedding Crashers (buddy comedy), Jurassic Park, (action/adventure), How to Lose a Guy in 10 Days (rom-com). All successful films, but in each scenario, the characters are secondary to the story idea. Imagine Twister or Jaws or Speed with completely different characters. The story does not change.
The second way to tackle a screenplay; however, is by creating an unforgettable character first, then listening, exploring, and learning from that character to allow a great story to emerge. With this approach, if you take away the character, there is no story, because it is the character (not the idea) that is the cornerstone of the screenplay. The character is the lifeline: the heart, the mind, and the soul of the entire script. Just look at academy award winners (and nominees) for best Performance by an Actor or Actress: Jeff Bridges as Bad Blake in Crazy Heart (2009), Kate Winslet as Hanna Schmitz in The Reader (2008), Sean Penn as Harvey Milk in Milk (2008), Daniel Day Lewis as Daniel Plainview in There Will Be Blood (2007).
There is no right or wrong way to give birth to your screenplay. If the story idea strikes, create characters that fit in the mold. But if it's the character that emerges, allow yourself to explore him or her. Put that character in different situations, different worlds, use character exercises to explore your character further, and most importantly, trust your character. A great character will lead you to a great story.