If this is the first script that you are actually going to make money from, forget about the WGA minimum, it's around $55,000 for the eventual sale to the production company. If you think you're getting anywhere near that for your first payment as a writer, you're dreaming. Most likely the independent production company will give you an option agreement. Which is basically them renting your property for a year or more. The option agreement will pay you in a five or six step process.
You'll get a couple thousand up-front when you sign the option agreement, if they are a legitimate production campany. Then you'll get $500 to $1,000 for the first rewrite. Then you'll get $500-$1,000 when they accept the rewrite. For the writer signing his first option agreement this is probably as far as it will get. But the option you signed spells out everything that you would get paid if the script actually gets made and released into theaters, then to pay-per-view and DVD release, all the way to television rights. If the script actually gets financed, you'll 1-2 percent of the of the final budget for the film when filming starts, you'll get another 1-2 percent of the entire budget when filming ends and the film is in the can. Then you can expect up to 5 percent of all NET profits that the film makes. Now this might sound incredible but the beancounters have many ways to cook the books that an independent feature that makes 300 million at the box office is recorded as a loss.
I think one of the most important steps for you now is to ask someone at the production company where your script is on their production slate. If it's in the top two or three there is a good chance that it's going to get financed and actually made. If it's below that there is probably no chance in hell it is ever gong to get made.