Best caliber for mule deer (out to 800 yds)?
6.5mm
.257"
7mm
.308"
I might get some hate for this, but here is my opinion:
6.5mm could be anything from a 6.5x47L to a 26 Nosler. From a good 130 to a 156. They will rock a muley, and recoil is not bad. So easy a kid can do it....
.257" could be a .250 Savage to a .257 Wby. But, I would go with a fast twist and heavy bullet like the 133 or 135 Berger to really capitalize on this caliber. Maybe a 115gr in a 1:10" twist, but 600 is getting about max for me with that combo. The heavies definitely hit above their weight class. Run those numbers.
7mm, I have never been a big fan of the smaller 7mms like 7-08 w. 140s even though tons of guys like them. So I would say 7SAUM, .280AI, 7RM, 28 Nosler etc. w. a 160gr-195gr bullet. Plenty for much longer shots, and can double as a good elk round as well.
.308 for me seems to start getting good in a .30-06, .300SAUM, .300WSM, .300WM, .300RUM. 180-230gr bullets. But definitely (for me), the big .30s are getting into that "overkill" range for deer, but dead is dead, right? Plus, recoil starts to really go up in a big 30 pushing heavies.
You could slip 6mm in there as well, but they tend to start to peter out at 700-800. The 105-115gr actually do quite well on deer-sized game. But out to 600, they work very well.