A rifle scope is the part of your setup that decides whether you get to take the shot at all. Most big game moves in the first and last thirty minutes of legal light, and that is exactly when cheap glass falls apart: contrast goes flat, the reticle disappears against a dark animal, and what you are looking at stops being useful information. The gap between a $200 scope and a $2,000 scope is almost never resolution at noon. It is low-light contrast, whether the turrets return to zero after you dial, and whether the thing holds point of impact after it rides 400 miles in a truck and gets dropped off a rock.
The other thing worth saying up front is that most hunters buy too much magnification. Big game in North America is overwhelmingly killed inside 300 yards, and a 3-9x, 2-10x, or 3-12x covers that with room left over. Crank the power up and you narrow your field of view, shrink your exit pupil (divide the objective diameter by the magnification), and amplify every bit of shake in an unsupported field position. A 42mm objective at 8x gives you a 5.25mm exit pupil, which is roughly what a dilated human eye can actually use at dusk. The same 42mm at 16x gives you 2.6mm, and the image goes dim no matter how good the coatings are. Buy the magnification your terrain justifies, then spend the rest of the money on glass and mechanics.
A note for the waterfowl and upland crowd, since this guide covers hunters broadly: your shotgun almost certainly wears a bead or a red dot, not a rifle scope. But the same people run scoped deer rifles in the fall, scoped slug guns in shotgun-only counties, and predator rifles in the off season. Where a rifle scope does end up on a shotgun, two specs matter more than anything on the box: generous, forgiving eye relief, and a recoil rating that accounts for the sharp rearward shove of a heavy slug load. Several picks below fit that job and are flagged where they do.