While 'buzz' can determine fitness though the email I can not. Elk hunting out west is physically demanding even if you deem yourself to be phsically fit the altitude and demands warrant doing extra exercise if you are used to the foothills of the east or less. While a 308 can be adequate, the ballistics necessitate placement and relative closeness (when compared with the cannons such as 300 Mag, 338, etc.). However, the cannons can cause flinch and inaccuracy to the veteran. I do not know your experience/skill level but it sounds as though your experience is low and skill undetermined. I would stick to a 308 or 30-06 as they *can be* relatively inexpensive to shoot and do not kick like a mule. Bolt actions tend to be more accurate than other actions. A base level 3-9X scope from a reputable manufacturer will give the right balance between cost and reliability. Paramount to a good scope is to have a good mount between your scope and gun. An associate of mine used to buy great scopes and do a shoddy job mounting the scope to the gun himself; I became the beneficiary of some nice scopes rather cheaply because he wouldn't heed my advice. He thought that the scope was bad and it wasn't. He finally understands now that his 'bad' scopes work so well on my guns. Have a knowledgable person about guns mount the scope to the gun.
A good place to haggle a good deal is at your local gun show. I buy my guns on
www.auctionarms.com and have the winning guns shipped to my trusted gunsmith/FFL dealer and have them thoroughly checked over. If you have a gunsmith/dealer that you can trust see if he knows of any guns. You can get cheap used guns at pawn shops but you don't know the history and the pawnshop is not necessarily a good gunsmith.
Are you going on a guided hunt? That permits greater opportunity to find and get close to the elk than going on your own especially if you are going with a lighter cartridge.
I wish you luck in your hunt for a gun/scope package as well as an elk.
As if you are not lucky in the first hunt (gun), don't disregard Buzz's suggestion of taking a camera as an alternative. While it won't be as exciting as a hunt, going with friends and capturing one of those magnificent animals in pictures has its own benefits.
Good Luck.