I'd normally advocate the 6.5x55 for anything that straddles the divide between predators and big game. The potential drawback being that, if your primary target is coyotes and wolves, you might be looking for a fur friendly bullet.
This is something the 243 can do, or at least, has potential to do a bit better than larger cartridges. Bullet choice and shot placement will still be important.
Further down the line I'd look at the 223 shooting heavier bullets in a fast twist rifle. The drawback being your rifle choice options might be limited, factory ammo choices might be limited, and the bullet choices might not be detachable mag friendly.
Which brings me full circle to the 243. Lots of good choices out there, no question, but this one fits well.