I won't shoot modern factory ammunition in any of my older rifles.
I load to M2 Ball specs for shooting through one of my 1903's or Garands. There is no need to send high pressure in older pieces of history. I got the load from an NRA publication years ago. I don't recall the charge but it used IMR 4895 and a Sierra 150 FMJ- I loaded Sierra Pro Hunter 150 JSP instead. That load is pleasant to shoot and has harvested Whitetail deer, So. Texas Feral Hogs, a few Coyote and one Maine Moose.
Be carefull Springfield 1903's tend to reproduce in gun safes....
I also have a "Low Number" 1903 bottom of photo (1910 mfg) Yes, I shoot it but I use a very reduced load with IMR 700X and Speer 100 gr Jacketed Plinker bullet.