If you really want to be silly, you can pull down your grandfather's .32-20 loads for his '73 Winchester and use those components.
Much easier to get some Hornady 150s or Sierra 180s or similar and load your .303 rounds to perform properly.
A good .303 should, off the sandbags, iron sights, shoot under 2 inches at 100. With a scope, that should go down considerably. But you won't do that with recycled SKS ammo, either.
The Russian bullets generally mike .310 through to .311. Extensive experimenting by the British over a period of 80 years showed that a .303 will nearly always shoot its best with a bullet at or very close to the maximum limit of size, which was .312. Some rifles even like fatter slugs than that, but generally with worn bores.
Enfield rifling (deep grooves, lands and grooves of equal width, odd number) tends to prefer flat-based bullets, even in the .30-'06 Model of 1917 rifle, so keep this in mind as you handload.
But you can get jacketed bullets from 80 grains through to 215 (formerly available in Canada, now being manufactued in Australia), which is pretty decent.