Each gun is different. But if it's a 1903 or 1903A3 Springfield I'd check the armory & the serial number.

Serial numbers below 287### should definitely be check before firing. Lead loads in rifles from the "bad" run are fine, but modern high powder ammo can crack the receiver.
Check on some shooter/collectors from National Match or Tuco's. You should be able an answer there. *Just don't give the whole serial number, cover it in a range or fuzz it like in this message.*

I have a 1903 Springfield with an old Leupold.
It's kinda ugly, but with 165 gr PMC or Rem. bullets. it's more than adequate for deer. I've never shot much of the military ball stuff (150gr FMJ) though that particular rifle, but you can't (shouldn't) hunt with FMJ anyways.