The primary source for original mission records for the California Missions are at the Mission Archives Library in Santa Barbara, where many of the original documents were centralized. I would start there.
Here are some addition sources used by mission scholars:
• Archivo de San Francisco la Grande, Biblioteca National, Mexico
• Archivo General de la Nacion, Mexico
• St. Mary's College, Moraga CA (Accounts for the Santa Cruz Mission)
• San Francisco Archdiocese Chancery Archive, Colma CA (accounts for Mission Dolores)
• Bensen Latin American Collection, Univeristy of Texas at Austin
• Bancroft Library at the University of California, Berkeley
There are, I am sure, important historic / original records in Spain but I have seen no citations to Vatican records. Most of the records for the Alta Calfornia Missions are in the U.S. libraries and museums I have cited or in Mexico.