I love the 308 at moderate ranges, I have a self imposed limit of 300 yards with my short barrel. I shoot 180gr partitions as I like heavy bullets, killed everything from coyote, bear, caribou. Easy to find brass or ammo.
"If it moves, tax it. If it keeps moving, regulate it. And if it stops moving, subsidize it."
I've used a 7mag most of my life but got a 6.5 CM a couple years ago and my daughter used it for deer in 2016. In 2017 I picked up my first .270 in a Ruger American. I am loving that gun and thinking about ditching the 6.5 CM. That .270 has less recoil than the braked 6.5 CM. .270 would be my choice.
I bought a 300 WSM in Sako Finnlight a few years ago for a sheep hunt and love it. It is 30 cal and hardly kicks and puts'em on the ground! It also is relatively light weight for hauling up and down steep mtns. It is plenty big for elk, moose, sheep, deer, antelope....a great all round caliber!
Your 308 choice is a good choice.
I have killed them with 243, 30-06, 300 WM ( wont ever use that again), 7mm, 8mm, 30-30, 12 Ga slug. Anything at or under a 30-06 is a solid choice- some ammo is easier to get than others, some rifles are lighter, some kick more etc.. My 300 WM just tore up too much meat. Some cal's have more forgiveness built into a not so perfect shot.
Your 308 is a solid choice
I used a .270 for a number of years and it served me well. Got a little grass is greener syndrome and ended up sending it down the road and got a 7mm-08, and honestly I think I have found my ideal deer rifle. Less powder, less recoil, and in a shorter barrel the ballistics are similar to my 270.
In all reality there are a lot of great mule deer cartridges, the .308 you mentioned in th OP being one of them. Find one that’s enjoyable to shoot, in a gun that fits and I think you’ll have your ideal mule deer rifle.