Church and Civil
In 1859, the civil registration law was passed in Mexico and standardized forms were used to record vital record information. But not everybody adhered to this law until 1867 when civil registration was strongly enforced. So to find birth, marriage and death information for persons who lived in Mexico, use civil records after the years noted. This will verify the place of residence of an ancestor as well. It will also verify family information. However, do not omit searching church records.
You will want to search in church records before 1867 and also after. Don't forget to make note of the witnesses at the registration or event. They may be relatives or friends which you may want to search for. By researching the witnesses at my great grandfather's baptism, I was able to connect the witness to my great-great grandfather and it led me to my gr-gr-gr-grandfather. What a find!