As for the calibers, I have always heard 270 would do for elk as long as you were good at placing your shots. Personally I shoot a 270 short mag and only one deer has ever not dropped on the spot, and that buck only went 10 yards, so I always feel the need to pitch it. 308 is a nice cartridge too, I prefer the short action myself, makes loading a lot easier in my opinion.
As for the rifles, I have had two great Browning X-Bolt Stainless Stalkers (one in the 270 WSM and one 25-06) and they both shoot and feel great. They have been kind of ammo picky though, but running Nosler Trophy Grade ammunition through the both they will drive tacks every single time. I have also been hearing rave reviews out of the Bergara B-14 rifles (which comes in both of your specified calibers). They are guaranteed sub MOA, walnut stuck, Bergara barrel, with their own custom made action. All for $800-$1000 depending on caliber and store.
As for the scope, I have a Zeiss duralyt scope on my predator rifle that is jaw droppingly nice. Fantastic clarity and light transfer, The next rifle I buy will get one. This scope will cost likely as much as any production rifle or maybe a little bit more, but I have always followed the adage that a cheap gun with a good scope is better than a good gun and a cheap scope.
Those are my two cents