The 35 Whelen is a proven big game killer in NA and brass can be easily made from 30-06. The rifles can be pretty light, it's not real expensive to reload, and you can plink with pistol bullets if you like.
The 9.3x62 is proven game killer in NA and Africa, and is just a slightly bigger brother to the 35 Whelen (6 grains more powder capacity and generally bigger bullets). Rifles are generally medium weight, it's not real expensive to reload, and bullets heavier than 300 gr are available. Downside is there are not lots of bullet choices out there, but probably 15-20, which is still pretty decent, and they do include premium bullets like partitions and Barnes TSX. 9.3 bullets tend to have a better BC and SD than most people realize too; better than either the 35 or the .375.
The 375 is more rifle than the others are, period. It's a proven game killer everywhere, period. But it costs more to shoot and hits the shooter harder as well, and the rifles tend to be heavier (Always in my personal experience...) and hold one less round. The rifles usually are a bit pricier than the 35's or 9.3's, since, for some reason, used .375's still sell for almost new prices, but you can get a good used 9.3x62 for $400 any day of the week. Bullet selection with the 375's is better than the 35's or 9.3's.
Based on what the OP stated, mostly shooting under 100 yards, I'd get a $400 used Husky in 9.3 x 62, run some 1F 30-06 brass through my dies, throw some BL-C2 powder in the case and top off with a Prvi 286 gr SP (Only $48 per 100!) and be good to go. This setup (rifle and ammo) would cost about HALF of th .375 option, weigh less, hold one more round in the rifle, and no way any moose or other big game will tell the difference at the ranges discussed.