Try the cheap Rem Core Lokts, in 180 grain. YOu can find them everywhere, they shoot amazingly well out of most rifles, they are cheap, and they hold up well on all game animals. Don't buy into the need for a "premium" bullet out of the 06. That said, I handload 180 grain partitions in mine, and love them, and am looking into other premium bullets for my 06. But I know, with certainty, that the 180 core lokts are hard to beat. my handloads squeeze out a little more accuracy, and I do have more faith in the partition, but have yet to see a heavy for caliber core lokt fail on an animal out of an 06.
This year, I used a Sierra Game King in my 2506 Tikka, did a number on my muley, I'll have to post a pic of the "perfect mushroom" that it did.