How important do you feel setting a rigid back story is for your character before you start to write the story you are trying to tell? How does this change when you change the mediums you are writing for? Say movie script v. comic book script v. short story?
Not at all important. Your character can develop nicely through the telling from tabula rasa. In fact, that gives you the greatest flexibility as a writer.
Like cognito said, you don't have to have one set in stone. There are plenty of ways to create backstory and bring it into play. I have always had a solid backstory for MC, but instead of info dumps, things are seen through other character's eyes, dialogue between characters, etc. All those techniques allow you to create your backstory without the infamous info dump.
I usually create a character profile following a standard template, from people i've seen. Things like eye colour, hair colour, accent, favourite foods etc.. Eventually you develop a bank of characters. The trick is to find ordinary people that could be extraordinary, a bus driver, your mail man, the check-out chick or maybe your dog. The next step i do is look at the idea i have, and the characters i have and see who would best fit(i have hundreds of characters). Now that you have the character in the story, you let them grow in it. The character template should only give you a rough idea of the character, but they should be able to change and adapt within your story. Perhaps your antagonist has green eyes but your protagonist has blue, yet you want the antagonist to be the father of the protagonist, you'd simply change the eye colour and their back story. I find you end up with more wholesome characters this way than any other way i've tried. Maybe I lack imagination
I personally like to give the character depth and story as I go along. The most I will do in the planning process is to create a name, place they've come from, immediate family, and occupation ... generally I let the character create the rest for me.
Before I start writing I always have the character's back-story in mind, but I rarely reveal it in the early stages. Better to let it tell and show itself as you write. It just helps me to know where they've been so I can know where they're going. I think it's probably different depending on the writer though. People I know can write with minimum planning, I'm often pretty stuck on the details.
BEFORE? Not important at all. Although I like to think that by the time my story is over, I'll know what my character's backstories are.
As far as I'm concerned, I'm a very meticulous writer, these days. I find it important to know almost everythng about my character before I start. I consider things like: gender, age, occupation, immediate family, culture, interests, and behaviors. These, of course, are flexible, but If I know them before hand it gives me a chance to create a character with motivations, with a history, with reasons. If my character were the next generetion of Batman [yes I did just see TDKR and do watch a lot of Justice League and read comics here and there XD] I'd want to know what kind of edge he has that makes him the right guy to be Batman. For that I must consider his young life and what kind of tragedie he's seen. Nothing is set in stone, some things you discover later, but that gives you a chance to rewrite for consistancy and/or, incorporate better ideas. NONE OF THIS has to be revealed right of the bat, but actually better off in sections and scenes. But how you introduce it is ultimately determined by the tone and voice you want to take. Flash Backs are great if you have a very introspective character.
Unless you have the story planned out in the greatest of detail, a complete description and backstory for your character will limit flexibility. At the other extreme, making it up as you go, you need to be sure you aren't inconsistent. A compromise would be to start with a vague idea of the character, and after writing each few chapters stop and update the character sheet with what you found to fit the story. Maybe the plot works better if he is left-handed, or flunked out of medical school, but you didn't know that until writing a scene. Don't lock it in until you use it.
