Question abt. the rifle...
Smith 357--Is this an original military '03-A3, or sporterized?
I have a dilemma in advising you. If original--At this point in history, there are only so many of these old war veterans left, and you should probably preserve it "as issued." And live with the military level of accuracy. OTOH, the Springfield can be made quite a bit more accurate by sporterizing as we did in the 1960's and earlier, so if yours is already bubba'd, you should be able to do better.
Some of these military rifles, just by happenstance, are much more accurate than the run of the mill.
My Springfield (actually a Remington) with its free-floated bbl and Timney trigger, not to mention cutting down the military stock and mounting a 'scope instead of the rear sight, will easily stay inside of 1.5 MOA. There were a zillion of 'em floating around, relatively cheap, when I bought mine as a starving college student who couldn't afford a "nice" civilian deer rifle.
Anyhow, a 165 grain SGK over IMR 4350 has done it for me for years & years. IMR 4064 worked good too. IMR 4320 not so much. I started using boat-tails simply for ease in loading. Recently switched to a 165 grain Nosler Accubond or Ballistic Tip, just because the SGK's lead tip gets dinged up in the magazine and in handling--otherwise it is an excellent bullet.