For me this is a no brainer for your purposes. I'd pick the 270 Win. Will cleanly take any of the animals on your list and shoots plenty flat, easier to find ammo than the 25-06, and won't smack your shoulder as hard as the 308 or 30-06.
I've taken game with all but the 25-06 and the 270 never ceased to impress me at ranges from "in my face" to over 400 yards.
That is my opinion but the final decision is up to you. Choose something that you are comfortable with and have confidence in. Either one will suit your needs.

I use a 270 for deer, black bear and coyotes (I'm not saving hides in this communist state as it's too much hassle). A 270 works well on all 3. As a bonus, using your deer/bear gun on coyotes gives you more live target practice in the field. If you ever go antelope hunting, a 270 works great on them also. I step up in caliber for elk and moose but that's my personal preference and not meant as a slight on anybody else's choices. Which 270 are you considering?

.30/06 is my choice. I have used mine for everything from headshots on jackrabbits and Canada goose (In New Zealand) up to moose and elk.

I'm a fan of the 270. A good quality 130 grain load that your rifle shoots accurately will handle everything you mentioned, at all the ranges you mentioned.

I also would go with the .270 for the simple fact it has moderate recoil, is flat shooting and very accurate and has a lot of knock down power.

Shot my (wife's) .270 today. What a joy to shoot. Busting clay pigeons from field positions from 10-100 yards. Could shoot that thing all day without feeling the recoil.

played with that in between working on loads for my muzzleloader.

Nothing wrong with the .270!
-Jake

If you were looking at bolt actions I'd have said the 25-06 but with a semi auto BAR, 30-06, ONLY way to go.