Saltillo is my hometown
Rental you have 2 options
1. Drive from MTY Airport using the toll road that will lead you to the Monterrey-Saltillo highway (toll too). Estimated time is 1:40. Airport highway toll is around $150 MXN and Saltillo Highway $80 MXN
2. Drive through Monterrey City. Saltillo signs are everywhere and Monterrey is pretty easy to drive. Estimated time to drive the city is 45 min and then Saltillo Highway another 45 min and $80 MXN
Since you're planning on driving next day morning, your only option is number 1 since traffic from Monterrey's airport to the city is awful in the morning
At what time do you arrive? Normally when I get late to MTY I drive to Saltillo
Other options not involving rental are: Monterrey Airport Taxi (I believe they charge like $1000 for the ride) or a bus which runs from Monterrey Airport to Saltillo
Let me know if you have any other questions