you can hardly go wrong with an accurate 35 whelen and 250 grain bullets, (mostly speer 250 grain)easily half the guys I hunt with have one, and every last guys been impressed with the results.
I have a remington slide action 35 whelen thats been the camp back-up rifle for years and that rifles, and its resulting kills in several guys hands has resulted in several people buying 35 whelens, Id be hard pressed to think of a better rifle for hunting the steep slopes and blowdowns
my late hunting partner preferred a BLR in 358 win, but either in skilled hands is a dependable elk killer