I would go ahead and get his service records, but typically they do not contain genealogy information such as the name of his parents or his family. But if you family history (oral and otherwise) indicates his name was Isom then I think you are on pretty good ground. I mean, how many Isom Beams could have been around at this particular time and place?
In those days, birth certificates were not in widespread use so I am not sure how you document a birth back then except by collateral documents that lend it support. Sometimes you can find an obituary for someone that gives lots of family inforation.
Good luck with the SCV aspect.