In search of ancestors

We took a wee run in the car to Carstairs and Carnwath in South Lanarkshire today. I know I have direct ancestors from these parts and wondered if I could find any gravestones that might prove to be familial.
We went into this wee church after the service had finished. The parishioners were so friendly. One of them even went back home to find a book she thought I’d be interested in and brought it to us a few miles up the road at another graveyard.