I had a coworker who paid $10.00 (plus shipping) for one like that... in 1962. DCM had previously graded their surplus rifles and priced them accordingly, up to $25.00 for a pristine one like that. But as stocks ran low they just lumped them all together and sold them for $10.00, luck of the draw as to what condition you got.
They are worth more, now.
well the box and any papers that it came with are probably worthless
I STRONGLY disagree, provenance from DCM/NRA will considerably enhance its value and interest. Mine came from Newberry's dime store for $36.00 and I doubt that its sales ticket would do much for it.
but you really need to start researching before you post. all remington 1903s were made using the double heat treatment process,
We all ought to do our research. Springfield did double heat treatment from 1918 to 1927, then went to nickel steel with a single step heat treatment. They did not stay in production of 1903s for very long but still some thousands of rifles.
Rock Island was a lot quicker on the draw changing to nickel steel after only a short run of double heat treatment in 1918. But they did not stay in production after WW I, their tooling eventually went to Remington to get them started making military rifles just prior to WWII.
When Remington started making 1903s they used a manganese steel (nickel was a strategic material in greater need for other products.) Although it was heated and slow cooled to anneal after forging, it was only heat treated with quench once. Around the time they went from 1903s to 1903A3, the alloy was changed to a chrome molybdenium alloy with carburizing in a single step.