Accuracy and power enough to kill what I'm hunting to the ranges I want to hunt them.
I want as much magazine capacity as I can get. When I'm meat hunting for deer, if I can get all of my doe on the ground from one group, the better for me. If I'm calling coyotes and a flock of them come in, I want them all on the ground. Load up in the morning, hunt all day without running out... That's what I want... I run 30rnd magazines on my AR's when I'm calling coyotes. My 6.8spc, I run 10rnds for deer (better feeding than my 26rnd mags). Upland hunting, I stoke 9rnds of 2 3/4" 12ga in the tube and start walking. Migratory birds (duck, geese, dove) are the only times I'm limited on mag capacity, which has happened about 4 times in the last 5yrs.
Trigger should be crisp, short 2.5-3lbs.
Weight isn't as big of an issue to me as handling and shootability. I almost never carry my rifle at low-ready while hunting anymore, even when stalking, so whether it's 7lbs or 17lbs, I just want it to be well balanced. I'm in good enough shape to hang whatever rifle I want over my shoulder for the hunting I do (rarely over 1/2mi from the truck, haven't been over 5mi from the truck in 5yrs).
Reliable and sure feeding, period.
Good optics. Clear, good performance across the gammut of low light to high light.
Stopping power good enough to pound DRT's whenever I put one on the button. Don't want to do too much meat or pelt damage, but I don't go afield undergunned.