Any of the 155-180gr range of target bullets will get you to 600yds no problems. Try a few and see what works best in your rifle. Mine loves the Hornady A-max's, but the Sierra, Nosler, Lapua versions will serve you just as well.
I've worked up loads for the 155gr Lapua Scenar (.508 BC) the 175gr SMK (.505 BC) and the 185gr Berger VLD (.556 BC). Although they have the least consistant O-give measurments the SMK's give me the best accuracy. I use 42.5gr Varget with a Rem 9 1/2 primer with Lapua Brass. This load will hold 1/4 MOA or better for three shots out to 300yds and 1/3 MOA for 3 shots at 500yds although I've had a few lucky groups that were better.
For the 155gr Scenar I use 45gr of Varget with everything else the same.
For the 185gr VLD I use 4064 (I'm way beyond the max load so I won't list my charge weight) for some reason they don't shoot well untill I reach very high velocites. I have a 1:10 twist Shilen barrel so it seems unlikely that I'm not stablizing them at lower velocties. I'm getting stamping on the back of the case, but no other pressure sighn. This is the flattest shooting (and hardest kicking) load I've ever shot through a 308 win.
It's generally pretty easy to develop accurate loads for the 308. They tend to shoot just about anything with decent accuracy.
I am still working up loads with mine but 42.6grs of RE-15 under a 165gr Gameking, or 42.0-42.1 of RE-15 under a 168gr Matchking seem to be shooting very, very well. at the moment all loads are.0200" off the lands and use a Rem 9.5 primer.
My Remington LTR loves the 168 bergers (sorted by bearing surface) with 43.5gr H4895, CCI BR2 primers, and neck turned Winchester brass. I can do half minute in all but the most extreme winds. No tellin what a good shooter could do.
