One of the better documentaries out there is A&E’s Titanic(1994). Narrated by David McCallum, it incorporates interviews with various Titanic writers, survivors and others. It was originally broadcast as a two parter and the original dvd release kept that order. Part 1 is Death of a Dream and Part 2 is The Legend Lives On. It is hard to find these days as it seems to be out of print. So either you buy it used or pay a huge price (over $200) for it new. Check out your local library, they might have it available to be checked out or able to retrieve it for you from another library in the system.
Fortunately YouTube has them available for view, but I cannot vouch whether the upload is legal or not. You can view the first part, Death of a Dream by clicking here. Part 2 is also available.
The dvd was repackaged for the Titanic centennial as Titanic: The Complete Story. It is the same, as far as I know.