As an update, I looked for other serial numbers close to the one you listed for your Grandpa and I found that there were several numbers within 2 or 3 hundred (or possibly more) that had been issued to the 8th US Infantry in 1900 or 1901 and a quick search of the 8th US Infantry indicates that they were, indeed, in the Philippines during that time.  I haven't yet found what role they had specifically, but I imagine that could be found with a little more looking.

I also remember that I had a close friend that had served in Korea during that war and he used to talk about rifles and such that they could buy in Japan (most of the guys spent a little time in Japan) while on leave or in transit to Korea.  So, it seems that your Grandpa could even have bought the rifle in Japan and sent it home as a souvenir.  It is too old to have been his service rifle.  If he was in the infantry, not an officer, he likely carried an M1 Garand, but in any case, it wasn't common for a GI to keep his rifle.

It certainly can be interesting to search for information about your Grandpa and his experiences.  It is always wonderful to keep our history alive and certainly, to see that our decendents are interested in finding the substance in a family 'story'.  Good luck to you on your efforts.