You will not find a better bang for your buck shooting long distance than 308 Win or 223 Rem.
If you shoot 308 Win, the Berger 168gr Hybrids are about the best choice today, they have a completely different profile than the old 168 SMKs and are stable in the transonic zone.
If you choose a 223 option, the 80gr Amax is about the best bullet you can get for long range. If you build a rifle on a Rem700 or Savage10 short action, you can load those bullets LONG for a Wyldle or CLE chamber to get get maximum case capacity.
If you wanted to go with something other than 308/223, you could pick any of the 6.5 family 6.5x55, 260 Rem, or 6.5 Creedmoor. You can launch the 123gr match bullets fast enough from those platforms to really stretch your legs.
But for "bang for buck" you can't really beat the 308.
Jimro