If the .500 S&W is not making your list, then the .460s&w has to come off of the list as well - it's only offering is in the same revolver as the .500, and everything "bad" about the X-Frame .500 holds true for the .460 S&W version too.
.454c and .480R should come off of your list as well, as these are grossly over powered for new handgun hunters. Recall, the 44mag is often touted as the most powerful handgun the average handgunner can be trained to manage effectively, and the .480 and 454c have 50-100% more energy than the .44, and come chambered in relatively similar weight revolvers.
.475Line comes off of the list, simply because all said above for the 454 and 480 apply, plus the added twist of no factory revolver being chambered for it.
I agree with the experienced handgunners above who have recommended you AWAY from the .357mag. It can and will kill game at very metered distances and under ideal shot presentations, but it is incredibly lacking for killing power compared to other more suitable cartridges. I'll point out, the .44mag has more energy at 100yrds than the .357mag does at the muzzle - that should not be considered lightly, and when you compare other killing power factors (Becker, wooter, Taylor, Hornady HITS, etc), the .44mag runs away from the .357mag even farther. The .357mag runs out of steam within a distance an average practiced handgunner could still connect on game, meaning you could hit game farther than you could ethically kill them. I have killed dozens of deer at short ranges with the .357mag, and have killed thrice as many with .44mags at much longer distances, including some past 150yrds. The difference is tangible.
So that really narrows us down to .41mag, .44mag, and .45colt. I favor the .44mag from this list, but any of these 3 can be effectively employed well both by a newbie as well as an experienced wheel gunner to kill deer as far or farther than they could ever make contact. I favor the .44mag because I started with one, but I can say it offers distinct advantages: the .45colt is only really on par for power in standard loads with the .44spcl, so you need specialty rounds or to reload to achieve 44mag level performance. The .41mag can't be loaded to the same power as the .44mag, and at the other end, it doesn't really have an available low powered practice cartridge. So the .44mag allows .44spcl practice and full power .44mag loads, both readily found in stores, while the .45 colt and .41 mag both require a lot more leg work to say the same. None of these 3 are a wrong answer, but in general, I recommend the .44mag is the most right out of these 3.
Ruger and Smith & Wesson get my money, customs like Dan Wesson or Freedom typically aren't on the menu for most folks, Taurus Raging line is good enough on a budget. I do the vast majority of my handgun hunting (which is the vast majority of ALL of my hunting) with a Ruger in one flavor or another.
Ruger Super Blackhawk in 5.5" .44mag with a JPoint sight and adapter under a Burris FastFire III, shooting Hornady 240grn XTP's will be serviceable for any whitetail deer hunter who ever walked the woods. Not too long nor heavy, very serviceable sight, and highly effective ammunition - the described weapon will kill deer for anyone willing to put in the practice to be proficient with a handgun.