I hate to throw a wrench in the equation. Have you considered the Browning X-Bolt? I've owned and shot the Tikka and X-bolt, shot the Win 70 (Not the Extreme) and the Bergara. They are all good rifles, I just really enjoyed the X-Bolt and got phenominal groups. I'd highly suggest that it gets considered, the Hell's Canyon Speed and Long Range especially!
As far as caliber, there is so much to consider besides the species hunted. Right now ammo availability is a factor. If that wasnt the case, or if you plan on reloading, then I'd confidently suggest the 6.5 PRC. 6.5 creed is a great round, but it is on the lighter side when you're talking big game like Elk. 300win mag is big, but there is no such thing as killing an animal "too dead" either. But 300 win mag isnt for everyone and some have a hard time not developing bad habits like a flinch when shooting magnums. If you think that may be the case, then you can throw a brake on it or maybe go with the tried and true .308 or 7mm, you cant go wrong with either and they are very versatile. .270 is awesome (even though guys say the 6.5 is better, they are similar and it's still a great round).
If I was forced to only pick one rifle caliber, I think I would lean towards some version of a .30cal. But that's just me!
Good luck - Remember it's not all about the stick, its how you wield that stick!