When most people are looking at civil records, they tend to head for the births and marriages. While these are filled with good information, the death certificate can be a wealth of information as well. But, and I can't stress this enough, it is not a primary source on anything but the date of death and cause of death.
Why you ask? This is a public record. Yes, it is, but, the person who knows the answers to some of the questions is deceased. You can't count on the person who gave the information to know the exact date of birth, place of birth and parents name. While Aunt Mable may know when her mother said she was born, she doesn't know it as a fact, she wasn't there!!
So, you have to keep this information and use it as a jumping off point but don't accept it as fact, just possible fact. Please note however who gave the information, this can be very important. It may also give the relationship of the respondent to the deceased.
When I was starting out, I began by using death certificates. They are the easiest and cheapest to acquire and they have enough information to put you on a path to follow.