Depending on the parts some of them may be stamped; those on original Springfield (and Rock Island) M1903s were milled. If you look on the right side of the rifle, the following parts should be marked with an R: upper band, lower band, moveable rear sight base, rear sight leaf, windage knob, trigger guard. If any of these parts lack an R they are replacements.
The Type C stock is a replacement. If you look on the recess for the cutoff (the ON-OFF lever) you should see a K or S stamp. The RA-P is an inspection or overhaul stamp from Raritan Arsenal.
Although I can't tell for sure, it appears the rifle is in the 3,048,000 range. If so, should have a barrel marked with a RA and be in the 1-42 to 2-42 range.
"We make men without chests and expect from them virtue and enterprise. We laugh at honor and are shocked to find traitors in our midst."