Some dates of birth would have helped a great deal. However, the rare first name of Orpah did make it easier.
The 1930 census shows David R. Beggs 31 (misindexed as Daniel) living with his widowed mother Orpha Miller 50 in East Chicago, IN. This census shows David's parents were born in Scotland and Wales.
The 1920 census shows David R. Beggs 20 living with his widowed mother Orphah Miller 40 in East Chicago, IN. This census shows David's parents born in England.
The 1910 census of Blairsville, Indiana Co., PA shows David R. Beggs 11, born in England, along with brother Jame 14 an sister Sarah 14, as the grandchildren of the widowed Mary Rauson 75.
The 1900 census of Pittsburgh, PA shows David R. Beggs, born March 1899 with his mother Orpah, born Feb 1880 living with her parents Wm Thomas, born Feb 1853 in Wales and Ruth, born June 1854 in Wales. Orpah was married two years. This census shows David's parents born in Scotland and PA.
Some of these records you can look at for free at labs.familysearch.org and Ancestry.com. For those you cannot see for free I suggest checking with your local libraries to see if they have Ancestry or Heritage Quest.
Here are some of the things you can do to find out who David R.'s father was. The problem is mostly in knowing which county the principals were born or married in. Pittsburgh seems like a good starting point. His birth may have been at the Allegheny County Register of Wills Office in Pittsburgh. Orpah's marriage to Mr. Beggs may have also been recorded at the same office. If David R. died in Pennsylvania the PA Dept of Health would have his death certificate. The record of David R.'s marriage may have data on his parents.
Check with the Western Pennsylvania Genealogical Society and the Historical Society of Western Pennsylvania to see if they can help you find his obituary and burial place.