I agree, the Model 70 in 338 Win Mag is a fantastic rifle/cartridge combination for the experienced rifleman/hunter. Might not be the best choice for the average novice. But recoil is subjective and no two people perceive it in the same manner. Most important is to have a rifle that you are comfortable with and can shoot well from any and all field shooting positions. Practice these until you can keep all of your shots within a 8" pie plate ( within 4" of your point of aim) from these various shooting positions. At whatever range you can no longer do so, this will be beyond your personal effective range. (I realize that the vital zone of a large moose is 12", but a deer is 8", and this will help you determine your effective range with your rifle on all big game). As for a scope, any quality scope in the 2-7/3-9/3.5-10 power range will work for moose. You do not need large objective lenses. Keep your rifle/scope package to under 8 1/2 lbs scoped, loaded and with a sling, as moose hunting can cover miles in rough and boggy terrain.
More moose have been taken in Canada with the 303 British/30-06/30-30 than any other cartridges. Cause they work!
They are big animals, with bulls weighing between 700 and 1800 lbs on the hoof, depending on subspecies and geographic location. But they are not overly tenacious of life and are easily taken at close to moderate ranges (50 to 300 yards).
In 35 years, I have yet to shoot one past 220 yards, and have used the 6.5x55, 6.5 Creedmoor, 270 Win, 270 Wby, 280 Rem, 7mm Rem Mag, 7mm STW, 30-30, 308 Win, 30-06, 300 WSM, 300 Win Mag, 338-06, 338 Win Mag, 358 Win and 375 Win. Any decent cup and core bullet will work, but recommend on the Alaksa/Yukon variety a premium bullet such as the Nosler Partition, AccuBond, Swift A-Frame, etc. as there is a lot more bone and tissue to penetrate to reach the vitals.
Best of luck on your upcoming hunting adventure!