+1 on a low power scope... 2 1/2 power fixed.
I hunted deer for decades this way. Started out with iron sights on a Remington 870 with a rifled barrel.
But the advantage of a low power scope is this:
It gathers light. So it extends your shooting light at just the time when deer are most likely to appear.
A second advantage to a low powered scope is this: no movements required. Sit totally still while you listen to the deer approach. Shoulder the rifle when its head goes behind a tree. Squeeze the trigger when its vital area emerges. No twisting of variable scope, no messing with binoculars. I always hunted from a tree stand or a ground blind, or else still hunting VERY slowly. I mostly hunted where the brush was so thick you couldn't SEE a hundred yards.
So it was more like bow hunting.
If you move, the deer dodges into the thick stuff... gone. If you fidget, you never see anything.
My experience with shotgun hunting is: shoulder the rifle, find the spot and squeeze the trigger in one smooth motion, or shoulder the rifle when the deer can't see you do it, and shoot when you have a clear shot.
You usually only ever get one shot. After I became a bow hunter, I switched to a 20 gauge NEF
single shot with a rifled barrel (& iron sights) during gun season. I had bought that weapon for
my girlfriend who expressed an interest in going "hunting with the guys..."
She did it too, and went to the range and shouldered that little gun and fired a decent group at 25 yards. But she decided that deer hunting was "pretty cold..." and only went a few times.
She gave me back the single shot... I went out and killed a deer with it. I decided a rifled 20 gauge shooting Remington Copper Solids was the world's best deer gun for brushy swales and corn fields. I would have mounted a low power scope on the NEF, except they didn't build it with that capability. It was a hundred dollar gun, the farmer's friend. Gunsmith couldn't drill it for scope. But that combination of weapon and ammo was deadly on deer... Every deer I hit with a copper solid went down fast.
With iron sights, just KNOW your effective range and don't take wild shots beyond it.