Free: Contests & Raffles.
I'm not sure what rifle brand/type you are looking at, but I've always wanted a Kimber Mountain Ascent in 308, threaded with suppressor. So I'm biased when answering for your stated purpose. I think 308 is a good fit for your stated need. Benefit in that you have other rifles in that cartridge. Choose a bullet that works for your intended purpose.For the 16"-20" barrel, a 7mm-08 would also be something to consider. There is the new 7mmBackcountry as well. But, if it were me I'd stick with 308.
In the context you defined I think the 308 is a great choice. I reload and have a 150 grain barnes ttsx and a 165 accubond from my suppressed 16" sig cross at 2700fps. Both give you elk killing muzzle energy out to 400 (1500 ft lbs). If you go out to 20" you might get to 2800. I have killed a few elk with that load and both drops em solidly. I also am liking the bergra line of rifles. My Kimber 84M in 30-06 is wicked accurate out of the box 1/2" moa and very light weight. Only thing with the lighter weight rifles is the point of impact shift from suppressed to unsuppressed. my 5 cents (up from 2 due to inflation)
A 16" barrel with a suppressor is very pleasant to carry around in the mountains...What bullet do you want to shoot? That's the real starting point. Back out from there. Minimum impact velocity needed for that bullet to perform will help determine barrel length. In .308 WIN you'd probably have to go lighter grain to make a 16" barrel realistic out to 400+.
This looks like it checks your boxes, and can be had for only $13k!https://www.gunwerks.com/fe