You probably want to look at Spanish immigration to Mexico (actually the Indies). See Catálogo de pasajeros a Indias durante los siglos XVI, XVII y XVIII. This is a set of several volumes. You can also see the original records at the Spanish archives website PARES at http://pares.culturaydeporte.gob.es/inicio.html
During the Spanish Empire permission to go to the Indies was necessary, although it didn’t always happen. This would have changed with Mexican Independence in 1821.
The thing to note with the Mexican Church records before 1821 is that they generally gave the ethnicity of the people the records referred to. When the term Español or Española was used it generally did not mean the people were from Spain, but rather ethnically Spanish (and usually born in Mexico) rather than one of the castas (Indio, mestizo, etc). In the marriage records if the groom was actually from Spain a dispensation was required as he was an “ultramarino.” The dispensation, if it still exists, will be in the diocesan records, and it will state where in Spain he is from. Sometimes, this info will also be in the marriage record. The ones I have seen were from the 1600s and early 1700s.
The diocesan records would be for the dioceses as they existed at the time, and not modern dioceses. The Diocese of Guadalajara was the important one for most of central and northern Mexico, over time it was separated into numerous other dioceses. These records are at FamilySearch, but are not indexed or extracted (although 3rd party websites with indices do exist).