I am currently working on a documentary and this will be my first project.

Is there a good consumer grade camera that would be suitable for filming a documentary?

I have Sony Vegas editing software, and have heard that this program can help with quality issues.

I have a very limited budget and I cannot afford to buy a $5,000 camera, or rent one for $500 a day.

It's much less about the quality of the video but the quality of the content for docs. People are much more forgiving for a less than stellar looking video if the story the doc is showing is really good. So I'd worry more about sound equipment and a camera that can shoot easily where ever you end up shooting your doc.