The "caliber/rifle" question is probably the most overthought "dilemma" on these boards. But, you started with a very solid suggestion out of the gate.

I'm not familiar with Savage centerfire rifles. They seem to have a fairly dedicated following, just as do nearly every other brand. Left-hand limits you a bit.

The .30-06 is likely the most versatile chambering on the planet. With bullet weights ranging from 110 to 220 grains, there isn't much on this continent that wouldn't be within your reach. Its recoil won't wreck your shoulder. Factory ammo is available everywhere.

Everyone is entitled to their pet elk round, and many of them do work well. In general though, magnums bring with them enough recoil to induce flinching. They're more expensive to feed, which for a budget-conscious hunter might make the difference between adequate and inadequate practice. The .270 is also a popular standard, but many view it as more suitable for deer-sized game. Again, and JMO, the .30-06 is your best balance between usable power and shootability.

If I were looking to outfit a rifle for an elk hunt, it'd likely be a synthetic-stocked .30-06. I'd top it with a quality mount and a 3-9x40mm optic. A good sling is an investment, not an accessory. I'd try to keep the weight down as much as possible. Stainless would be okay, but I've never had an issue with blued finish.

Elk hunting is physically demanding. Good boots are a must, as is a fair degree of physical conditioning. I've never walked as much for any game as I do for elk. That's a huge part of the challenge and the fun. Carry what you'll need to dress an elk and basic survival gear, but keep your pack as light as you can.

Be ready for some breathtaking scenery and a hunting experience like you've probably never imagined!