Dana, You have an interesting time ahead of you as you research your James C. and William Murray. Try to work backwards from them. Do you have wives for each? What state did they die in. Do you know what state they were born in? If your grandfather William had brothers and sisters, you may learn good information by going "sideways" as well as backwards. Do you have cousins? Someone in the family may have already done genealogical research and be willing to share with you.
Sarah Murray Byrd Childers was born in Virginia in 1801. There were many of her family in Virginia and Kentucky. People didn't move quite as much in those days and it is always a benefit when a family stayed put in the same county.
See if you can pull up information from the SSDI - Social Security Death Index on your father and grandfather. That may be a good start. If either of them were in the service, you may find something in those records.
Happy hunting! Mary