You are limited to 5 round magazines in Oregon for most (maybe all) hunting purposes.
I have a Remington R25 (AR 10) in 308 caliber. If you're comfortable with the M16/M4 platform you will take to the R25 (or any other AR10) with ease (18 years in the Corps, they're comfortable). But they're not a 5.56 weapon so there is a significant weight penalty. It does however, have a full floated barrel and factory "Mossy Oak" camoflage. Mine also weighs a ton because it has a bipod and 6-19 lighted mil dot scope. It will take any critter in the Americas.
Book specs: 20" free floated barrel, calibers 243 Win, 7mm-08 Rem, 308 Win (7.62x51 NATO works as well). Single stage 4#2oz trigger, 4 round factory mag (20 rounders available online), Picatinney flat top, Picatinney topped gas block, Overall length 39.75", Length of trigger pull 14.125", Wt 8.75# (that's just the bare rilfe), MSRP 1567 (but you canget one cheaper).
This rifle is NICE but it is HEAVY....wanna hump it through the woods all day?
My Carbon 15 (Bushmaster AR15 with Carbon Fiber upper/lower and collapsible stock) weighs in at just 6 pounds 9 ounces WITH 25 rounds in a 30 round mag and a red dot scope. (the R25 maxed my small kitchen scale so I can't give you an "all up" weight on it).
The AR15 (5.56/223) is legal for deer but I'm not sure about Elk. I certainly wouldn't use it for Elk and consider the 5.56 to be inferior for deer as well while it will work (my grandfather used to take them routinely with a 22 long rifle and damn good shot placement). One thing to note is that the heavier bullets available for the 5.56/223 (if you handload) won't fit in the magazine and have to be hand fed so the bigger .224 bullets negate your having a semi-auto.
What's nice about having the AR10 and the Carbon 15 is that the AR10 is kind of like a weight machine for the AR15..... The 15 really feels like it's floating after you handle the 10 for a while.
What I use for deer is a Winchester 1894 lever action in 45 Colt with a 250 grain lead flat round nose or Hornaday 250 grain XTP jacketed hollow point. I hunt where shots are 50-100 yards max though. I'm sure it's capable of taking Elk but I wouldn't use it for that purpose due to the massive drop of the bullet and rapidly disappearing energy beyond 100 yards.
My long range and Elk rifle is a Weatherby Vanguard bolt action in 30-06. This will also take Elk (or anything else you want. I call it my "AT&T" rifle as it will reach out to touch something.
The R25 is in the 12-1400 range new.
The Carbon 15 was 599 (609 out the door) with background check, 2 30 round mags, case, and a Busnell red dot scope (I think their normal was 799)
I think the Vanguard was around 500, just the rifle.
There are a lot of rifles that will work well for deer and Elk. A lot depends on whether you are wanting a rifle that will double as a self defense system, whether there is any chance of going back to Kali (the AR platforms are mostly verboten in Kali), your budget, and of course personal preference.