I'd got with the .260 myself. In the 6.5mm bullet line, you can get light 85gr bombs up to heavy 160 grain freight trains. The problem for me is the very limited availability of .260 factory ammo. I don't reload at all. I hardly have the time to just get and shoot, much less reload the ammo too. (Wish I did!!) Fabulous ballistic potential, low recoil, superb accuracy. Liked others have stated, though, it wouldn't be a "shoot all day" gun like one of the .17, .20, or .22 centerfires.
My "Ultimate" deer/dog rifle in my mind has long been a Remington Model 7 in .260 with a stout 22"-23" barrel, something with a .675-.700 muzzle diameter and a magnum contour to the taper. Fluted barrel, maybe, it looks cool, but wouldn't be an absolute must. Slap it in a qualiity stock like a Bell & Carlson, McMillan, etc. It wouldn't be light (for a M7), but it would be about as compact a bolt action as you can get.
I'd put a set of quality detachable scope mounts on it, with 2 scopes. One would be in the 2-7 or 3-9 range for deer and big game, the other would run 4.5-14 or a bit bigger for dogs. Both would be the most compact scopes I could get to keep the rig balanced.
Anything thing I hunt would be in extreme danger out to 400 yds, and I'm not going to shoot any big game past that (probably not even 300 yds, unless I was getting in a lot of practice beforehand). A 140gr bullet of extreme sectional density at good velocity will drop anything from a moose on down for me. I would not use it for big bears, unless it was a life threatening situation of last resort.
A lot of custom builders hold the capability of the .260 in high regard. I once read an article in one of the tactical shooting magazines that quoted George Gardner (GA Precision Rifles) something like "friends don't let friends shoot .308's, when there's the .260 instead." (I love the .308 too.)