Heh I was just mulling over this last night, good coincidence. This is what I made notes on, anyone is free to correct or add to.
From multiple books and journals I've read, snipers would always
try to get the best quality ammo issued or floating around in the field.
I just also read in the new Matthaus Hetzenauer biography that just released, that it wasn't uncommon to use armor piercing 8mm ammo for punching through armored machine gun nests, and
using tracer ammo for testing ballistic effects at high altitudes.
From senich's book says a specialty produced sniper round 'effect firing s.S patrone" was made later in the war.
Then there was the B-Patrone observation round with it's controversial effects, which you probably know...
The variations page for the 8mm Mauser on wiki says some other ones that had some favoritism with snipers were:
Anschußpatrone "sighting-in" round used for sighting in rifles.
And I personally love any yugo M75 post war stuff I can pick up.