Anything that keeps a good .277, 7mm or 30 cal hunting bullet moving at a sufficient velocity at your intended max range will work. Lots of elk fall to short action non-magnums like 7mm-08 and 308 every year. Plenty also fall to 30 cal and larger magnums like 300 win and 300wsm and even 338's.

Build whatever you trips your trigger and that you think you can spend enough time behind the trigger on. Based on my experience out west, I would spend maybe 10% of my range time at the bench and the rest getting myself completely out of breath and then finding the least comfortable position possible and putting 2-3 on target as quickly as possible. It's more about shot placement and making the shot with elk than caliber.