Free: Contests & Raffles.
I believe that with a .270 you can take just about any animal you are going to come across in washington, recoil isn't bad and they can barely fairly inexpensive to buy and shoot. The problem with rifles and one of the most expensive parts of hunting is always what glass you are going to put on it.
Definitely go with a 7mm-08, or a .260. I have a couple 7-08's and a .260 and love them all. You can use 120's for deer and 140's for elk. With my .260 I can watch a bullet hit the target (usually an animal) through the scope. Pretty awesome. My .260 is a Stainless ruger M77. My 7-08's are a 700 Rem and a TCR 87. Recoil is mild in both calibers.