I live and mostly hunt in an area where only shotguns and muzzleloaders are allowed. I feel very blessed to have (3) shotgun/sight/load combinations that have never let me down on deer. That makes it difficult to pick a favorite, so I will list them all, but I will call it a tie between the first two.
1) Ithaca model 37 pump, 16 gauge deerslayer with Weaver fixed 1.5x scope. This one has killed my two biggest antlered bucks and most overall. For my first 15 deer seasons, it is all I used. I killed the first deer I shot it at when all it had was open sites, but missed the second. After that, I put the Weaver on it and have been 100 % ever since. That is around 40 deer, mostly killed with Remington 16 ga "sluggers". This combination groups about 6" at 75 yards which is what I would consider the limit of it's effective range. I did strike my largest buck with it from 110 yards, outside of the vitals, but fortunately I was able to run him down and put him out with a followup shot from point blank range. I don't use it a lot these days, preferring the longer effective range of #2, but I did take my second-largest buck with it a few years ago when I brought it out. I could have shot a smaller buck with it on the only hunt I carried it last year, but he would not take 2 more steps to get off posted land.
2) Marlin 512 slugmaster bolt-action, 12 gauge with Bushnell banner fixed 3x scope. This is my primary gun now. It will consistently hold a 2" group at 100 yards with 2-3/4" Hornady SST's and my longest kill with it was at 163 yards. We are allowed to take up to (4) antlerless deer and (1) antlered per season here. This gun/scope/load has killed every deer I have shot it at but unfortunately none of them had antlers. Hopefully that will finally happen this fall. I have passed up on a fair number of smaller bucks with it, so that I can save my tag for another zone where rifles are legal (I also have one of those that has got the job done every time and has accounted for most of my bucks in recent years).
3) Remington 870 pump 12 gauge, short smooth-bore barrel, open-sights, 2-3/4" foster slugs (various makes). This is what I carry when it is raining or snowing, and windy because I do not like a scope in those conditions. I held a 2" diameter 3-shot group with it at 50 yards on the range last fall with Brenneke KO slugs, which was slightly better than most years. I have killed every deer I have shot at with it including 3 or 4 with antlers and more does than I can remember. All but one were under 75 yards. The spike buck that was at 100 was broadside, feeding on clover when I noted the mud fly over his back telling me my first shot was high. He looked up, then went back to feeding. I used the "artillery correction" method, lowered my point of aim, and my second shot hit his spine and put him down.
Prior to getting my Marlin bolt action, I tried a Hastings rifled barrel with a cantilever scope mount and a 2-7 Redfield scope on this gun. That combination let me down big time, hitting a few deer far from where I aimed and missing one clean. I was able to determine the cause of that trouble was deflection of the cantilever mount, dependent on the temperature of the barrel. You could actually watch the shots walk up the target as the barrel heated up. I traded that barrel for a 50 cal T/C Omega ML, put the Redfield on that, and hunted with that as my primary gun for about 5 years, while having the 870 with open-site barrel in my stand/blinds for backup. That is the duty where it notched most of its kills. I had several (2) deer hunts where the ML took the first one and the 870 the second. Now I just carry the Marlin 512 which packs (3) slugs, allowing for multiple kills with one gun.