The new M-70s are excellent rifles and the .338 Winchester is certainly an accomplished big game cartridge, but the most important factor you need to honestly evaluate is your shooting experience. Just because you're a novice moose hunter doesn't mean you're not an accomplished marksman, but if you're not, the .338 is not a platform that will benefit you as a novice rifleman. The fact of the matter is, when folks ask for cartridge recommendations, its frequently because they lack the practical shooting experience to make an informed decision, and have almost no experience with cartridges of more power than a .308. If you have little shooting experience, and if you aren't likely to shoot 500 rounds per year, a cartridge with less enthusiastic recoil might be better suited to you. A .30/06 chambered in a standard weight rifle, might be the right choice, and is almost certainly the most power you should consider . With a good 180 gr bullet, like Nosler's Partition and Accubond, its a flat shooting, hard hitting, accurate cartridge. It still barks and bumps the shoulder when fired, so its better if you could try one out before spending your hard earned money, then finding out its too much of a good thing. Should that be the case, cartridges in the range of 6.5X55 up to the .280 Remington are all viable, but when loaded with bullets of equal weight, its unlikely you could differentiate between a .280 and a .30/06.
This is usually when I suggest that someone getting into the centerfire rifle game take up handloading at the same time. Handloading allows you to make ammunition that is tailored to your needs. If your find that recoil is unmanageable, you can load lighter bullets, and lighter powder charges to improve the rifle's manners, then you can work your way up to the more powerful loads as your tolerance to recoil increases. The handloader can also load ammo tailored to various uses, thereby making his rifle more versatile. You could carry a few rounds, identified by the bullet loaded in them for small game or game birds to supplement the camp larder. If you are a pelt hunter, FMJ bullets reduce pelt damage. Meanwhile full powered heavy for caliber bullets are suitable for the largest game you're ;likely to encounter. Naturally loads with lower velocities and different style of bullets impact differently that your standard hunting ammo, but if you choose a scope reticle that has multiple aiming points, you can correctly hold for your specialty ammo.