1 gun only? 30.06.
Multiple guns? Use a .243 or a .270 for smaller game & a 300 Win Mag for bigger game.
My guns? Use a .243 for deer. Use a 300 Win Mag for elk. Use a 375 H&H for caribou & elk.
My thoughts? You need KNOCK DOWN power for most hunting in Washington. Primarily due to one overriding factor. Too many hunters. If you shoot (and kill) an animal with a small caliber, that animal will likely run a few hundred yards, perhaps a 1/4 mile before it lays down to die. During that run, the CRACK of your rifle will awaken all the other hunters (because the report is so near) and one of those hunters will put another round in your (nearly dead) critter. That hunter will tag your animal. So you better have a rifle with knock down power, to drop that animal in it's tracks. And that takes weight. A .270 simply doesn't have enough bullet weight to drop a big game critter. Oh yeah, it'll kill one just fine, but you'll have to track it for a while. I think the minimum bullet diameter for a big game critter is .308 (30.06). But getting a smaller bullet is tough to find on the big cartridges, so the ought-six is a great, all-around gun.