I received a question from an applicant today who wanted to know if she should send obituaries, headstone photos, cemetery records, etc for an ancestor for whom she has a long form death certificate that includes parents' names, spouse name, and all the other information we look for.
The answer is "it depends!" For a person for whom you have not only the long form death certificate but also have a birth certificate and perhaps even a marriage document that includes parents, then the death certificate is sufficient.
For a person for whom the death certificate is also your main source for birth information, I would include everything you have. In these situations, I also try to find census records that show the person in the household of his/her parents. The 1900 census should always be included if applicable as it gives month and year of birth and can corroborate the birth information on the death certificate. If you are not sure, then send it all. I may not use it all, but let me make the determination.