My advice to any deer hunter is to choose any gun legal caliber and practice a ton. First day of deer season sounds like the gunfight at the o k corral. Learn to shoot your gun accurately. Since I am limited to your choices, I'd choose the 12 gauge. All four choices are acceptable deer guns, just learn to hit what you are aiming at, all the guns listed have and will kill a deer.
Marlin 44. The picture in my profile is a buck I took with mine. 10 point 140 inch and 163 lbs. It went about 30-40 yards before piling up. Its easy to shoot, you can shoot it a lot on the cheap. It is more accurate than any shotgun that I ever used, and at least as accurate if not moreso than my muzzleloader. I shoot about a 2 inch group at 100 yards.
Any will work with proper shot placement. Which do you shoot best? For me it would go down to the .44 and the 20 ga. Just cause I have not gotten a deer with my marlin yet and have never used a 20 for deer. I am not a fan of the .357 for deer, but realize it works andothers can do well with it.
.44 all day long. (240 gr. XTP) I switched over to a .44 Ruger carbine a few years back and not only is ammo cheaper but recoil is less than a 20 Ga. Have a 20 Ga 870 with cant. barrel and took the time to compare both, ran several varieties thru both and have definitely settled on the .44. Have shot several deer (7 to this point) with the .44 and not one has made it past 50yds. Only drag is if we participate in Military hunts they won't allow any rifle cartridges so need to keep a good slug gun as backup.
I bought the Marlin in .357 a couple years ago specifically for deer hunting and it's perfect for my needs. I have a Ruger Blackhawk in .357 and wanted to keep the same caliber. I use the iron sights and can reliably make a kill shot on a 50 yd target. The longest shot taken on a deer was 40 yds. No problem. I primarily like to bow hunt but if it's primarily an issue of putting venison in the freezer quickly I like the Marlin.
I'd do the .44 mag with leverevolutions. Plenty of power for deer out to 100 yards, not as much recoil (hence easier to shoot accurately), and much handier to carry around in the woods.
I hunt with a Marlin 44 Mag. I would never go back to a shotgun, little recoil, really good accuracy and it's just plain fun to hunt with! Rounds are quite a bit cheaper than good Sabot slugs as well. I shoot WWB 240 Gr. JSP and they are an awesome deer round. I have always had pass thru shots. The ammo is about $35 for 50 and Sabot's can cost upwards of $15 for 5 plus you will probably shoot the center fire more in the off season and be able to get really accurate with it.
It seems pretty hard to come by a good Marlin in 44 or 357 these days (especially at a reasonable price). Rossi makes a good one at a more reasonable price. I don't think Marlin is supposed to pick up manufacturing those models again until the end of first quarter, 2012.