One of the most beautiful cemeteries on Staten Island is at The Church of St. Andrew, Episcopal Church.
If you are researching ancestors possibly buried here, you will want a copy of The Church of St. Andrew, Richmond, Staten Island;: Its history, vital records, and gravestone inscriptions, by William T. Davis, Charles W.Leng and Royden Woodward Vosburgh. I am lucky enough to own an original copy of this work, inscribed by Davis.
But maybe a better buy is another more comprehensive volume that includes the original Davis work as well as the records of two more churches. This more comprehensive volume is Staten Island Church Records [Records of the Dutch Reformed Church of Port Richmond, 1696 to 1772; United Brethren Congregation, Commonly Called Moravian Church, 1749-1863; and St. Andrews Church, Richmond, 1752-1808], edited by Tobias Alexander Wright.
The Church of St. Andrew has been digitized by Ancestry.com, and full page images are available. This wonderful because you can see who’s buried near each other, and you are treated to the full epitaphs. Staten Island Church Records is also available at Ancestry, but only in index form; without the full context it not as useful. I’m also not quite convinced that their search identifies for you which of the three churches the records came from. So I use a hard copy as well.
This church, founded in 1709, is still an active parish. See the Church of St. Andrew website for a brief description of its history.