I am looking to start up a video documentary company (taping older
people about their life, weddings, etc.) and was curious if there were
any resources out there detailing what the general costs would include
to start such a compnay. For example, cameras, lights, editing
equipment and the like.

Also any general information pertaining to video documentary companies
would also be appreciated, i.e. competition, common problems,
profitability, target markets, etc. I?m not sure if any of this
information is out there because most of the companies which do this
are small and private, but any info is appreciated.

Check out http://www.reelbiography.com
Their website lists prices, types of video bios they do, samples, etc.
While it won't answer many of the questions you listed above, it's a
trove of good information.
Even the desing of the website itself is impressive.