Is your father still alive?If so, are you in contact with him?Find out as much as you can about where your father grew up, went to school, etc.Was your father the oldest child?If so, on average men have their first born childn in their early to mid 20's.
If your dad was born in 1937 minus 20-25 yrs would make your grand father born ca. 1910-1915. He may have registered for the draft in WWII.He should have a marriage record.He should have a SS death record, which you can order and may have John Richard's parents names, if not at least it would have his date of birth and where he was born.
Have you checked census records for MS for John Richard Murphree?
Do you know of any family Bible?Are you in contact with your aunts, uncles? Do any of them know anything?You will be surprised how much people know when they think they know nothing, you just have to get them talking about the "good old days."
If you live in Quitman Co., you can go to the courthouse and request to look at marriage records, birth records, etc.These are all public records so they have to let you look through them.It may take some time, or you may hit lucky and they have all been transcribed.