Slee did a good job of describing the rifles, I'd go with a bolt action and look to pawn shops or ask around there should be no problem getting a 30-06 bolt action for around $200, they are common and if your not afraid of having a used gun I'd go that route. The lever gun like he said is good for under 150 yds. I still use a 30-30 lever on occasion for both Elk and deer when I'm hunting the extremely brushy west coast areas, they're nice and short and quick to bring up especially when not using a scope. But if you plan to hunt more toward Cle Elum, I'd go with a distance gun, that '06 will do nicely and you won't have a problem dropping an Elk out to 400+ yards with it. LEt me know when you get home, I'd be happy to run around and help you find a gun too. Also if you do plan to deer hutn say in Cle Elum let me know we usually have a big hunt party up that way the opening week.

Another thing to consider is keeping in mind if the gun you like doesn't have a scope, you'll need to budget that too if your inclined to using one. You can get a decent scope for around $200 also, brand new, I just bought a Weaver a couple years ago for $190 and I love it as much as a Leopould myself....FYI