There's a lot of common sense in the above choices. Especially as most place the 375H&H last. It can really be an ornery mule in a light rifle.
The ability to handle recoil is an acquired taste. The more you shoot the more recoil you can tolerate. If learning to shoot powerful rifles is a skill you wish to acquire, you must shoot frequently. The more powerful the cartridge the more important it is to have a rifle that fits you well, and the more important is the investment in a high quality recoil pad. The rifle that has hurt me the worst was a stock Moisen Nagant 7.62X54R carbine. I often wondered what the Russian's had against their own troops.
The various .375s are well within my tolerance limits, although towards the upper limit when shooting groups slung up prone. I can manage 5 shot groups prone where I can only manage 3 shot groups with a heavy loaded .416 Rigby. Over an afternoon shooting prone becomes tedious, but as a rule my groups don't open up when load testing and on the days they do, its time to call it a day. Beating yourself to a pulp achieves nothing but cause your skills to diminish. The proper shooting position when first exposed to firing a powerful rifle is off hand at short range. Felt recoil increases as your position becomes more solid; off hand is less intense than kneeling, kneeling is less intense than sitting, and sitting is less intense than prone. Locking yourself into the rifle with a shooting sling from a rested position assures you will get the most bang for your buck, but it also makes hitting your target easier and keeps your groups tight once you've realized that recoil doesn't matter.
It seems that with the exception of the most deranged of us, a light weight .375 is carried more than it is shot. This is unfortunate because the more the .375 is fired the faster the shooter will realize that it is as fine a performer on the range as it is in the field. When you are hunting it does not normally require more than a shot or two to get the job done, and if you are fit enough to play contact sports, recoil from a powerful rifle shouldn't matter to you. However if you have convinced yourself that the .375 is a brute before you ever pick one up, the chances are it will master you, rather then are the chances that you will develop the skills to master it. The proper mind set is, "These things are designed to be used effectively by normal people, and I can do it."
The Ruger Alaskan chambered in .375 is a wonderful package for North American hunting under difficult conditions. The rifle is light enough, accurate, reliable, powerful, and affordable to own and shoot, compared to other powerful rifles. It doesn't recoil as strongly as my .375 Ultra, although you may have to shoot both rifles side by side to tell the difference. The least affordable and the most difficult .375 to master is the .378 Weatherby.
The .375 can shoot as flat as a .30/06, it can be legally used on dangerous game over seas, and yet handloaded with Unique it can take small game with no more damage than one would expect from a .22. When working or playing in big bear habitat it is a great source of comfort in the protection role, particularly if you are responsible for the safety of other people. In addition to that it will efficiently take all manner of big game with less damage than we have come to expect from high velocity small bores at normal hunting ranges.
If you are a gun crank who finds the allure of powerful rifles intoxicating, the .375 is a good place to start. Many African PHs are pleased to see their clients arrive with a .375, particularly an H&H, as the relatively light recoil means that there is at least a hope that the client can shoot well. They cringe when a client gets off the plane with a shiny new (read untried) .460 Weatherby. If you are going to shoot the cartridge enough to master it, you must handload for it of course. This will allow you not only to an affordable supply of ammunition in sufficient quantity, but it also means that you can begin with moderate loads and work your way up the power scale. However, the lessons learned from shooting a .375 will bode well if you have the opportunity to hunt with and/or shoot truly powerful rifles, that to mind mine begin with 570 grs at 2100 from a .500 Nitro Express.
The .375s have something in common with the .30/06. That is they are so versatile that if you have one, there is little reason to own anything else.