If you are not recoil shy, then I'd go with a 7MM or .300 magnum.
However, ( and I know this may upset a few magnum pushers)....
with good shot placement, at reasonable ranges, anything from the 7MM-08, .308, .270 and 30-06 will be fine for elk.
As for the gun, Winchester, Remington and Savage, as well as a few others make great shooting guns at reasonable prices!
Scope, Leupold!