Hello Richard,
Your grandfather wasn't a full-time professional soldier; he merely pre-empted the call-up for national service which he would normally have started in October 1910. I can't remember whether there were benefits to volunteering early.
Ancestry is of limited use for researching German ancestry. They have some excellent collections for Hamburg, Berlin, Hessen and the Bavarian Miliatry records, but unless your ancestors came from those places you won't find much in the way of primary records.
Geni and MyHeritage are only platforms for people to publish partial family trees. They may help to suggest research paths, but they were not intended to be a substitute for normal genealogical research via primary records.
My own patrilineal ancestry, which I have been researching for about 18 years, was also German Jewish. Although the family has roots in Bavaria (Lower Franconia), they moved to northern Germany and my great-grandfather came to the UK in the early 1870s. However, he had many relatives who stayed in Hamburg, so my British paternal grandfather (a Catholic!!) fought against German Jewish cousins in WWI and, of course, lost relatives during the Holocaust. One such cousin was also awarded the Iron Cross, taken prisoner by the French in 1916 and subsequently deported to Riga in 1942 where he and his wife perished.
The first thing you must do, if you haven't already, is join JewishGen. There you might even make contact with other Oppenheimer descendants.
Going further back, you will need to obtain the usual birth and marriage (and maybe death) certificates from the responsible registry office (Standesamt) - but only as far back as 1874, registration records from your ancestor's towns of residence from the appropriate Bavarian archives, etc., etc. There are probably a lot of records available, but not at the press of button.
There are other records relating specifically to Jews that I can point you towards when you get into things.
I'd be interest to hear about your father's side. You can always send me a PM.
Justin