I prefer the .458 Winchester to the .45-70, as it can be loaded to any power level you like, but you can't beat the Marlins for for handiness. The .444 rates much lower in my estimation as it is commonly loaded with pistol bullets. A good hard cast .429 bullet in the 300-350 grain range would help this round significantly. The factory loaded .458 Winchester is either too powerful or has unsuitable bullets for your needs, the .45-70 is anemic as factory loaded, and the .444 suffers from bum bullets - so if you choose anything from this selection you do need to handload your ammo.
I find myself in reluctant agreement with those who champion the M-7 350 Magnum. I have owned several 700 Remingtons - some fed well, some fed poorly - my .350 mag was one which happened to feed well. If I was going to go this route I would be more inclined to have a gunsmith built bolt gun - probably on a '98 Mauser - rather than an off the shelf model that I would have to tweak into shape by trial and error. A Remington custom shop rifle should do as well, but this is an assumption - I've never owned one.
A medium bore round which is getting more North American attention these days is the 9.3X62. With it's moderate velocity, light recoil, and heavy for caliber 286 gr. bullet, it would be an excellent bear/moose gun, with a bit more horse-power than what is available from the .350 magnum.
My person favorite in the medium category is the .375. It combines flat trajectory, moderate velocity for good bullet performance, and manageable recoil - if at the upper end of manageable for a seasonal shooter. There are nearly as many bullets available in .375" as there are in .308". There are an incredible number of .375 H&H rifles to choose from - for all budgets from poppers to sultans - in all sorts of configurations from long barrel African plains rifles to Mannlicher carbines. If you are in a part of Newfoundland which has the occasional visiting white bear, a .375 might be your best option.
If the rifle is to be scoped, I prefer a fixed power scope less than 3X, but a variable in the 1.5-5X, 2-7X or 1.75-6X are all compact with generous eye relief. If the rifle is only going to wear metallic sights, a ghost ring and post is my preference. The ghost ring should have a very thin rim and a aperture of about 1/4". If the aperture sight you buy has thread-in thick rim apertures, sighting without them will provide an aperture of approximately the correct size. The post can be had from any number of commercial suppliers, but I had mine made from a piece of brass stock, which appears white when set against a dark background and black when set against a light background.
