I got my 375 H&H this past year and it shoots like a dream..I can use it for big game, i.e. brown bear, moose, and even deer for those 300yd shots. I am planning a brown bear/ sitka deer hunt in the near future and this gun will fit the bill perfectly.
I own several 300wm but wanted something with a little more if you know what I mean. Like you, I pondered those other calibers but settled on the 375 after talking to many guys I know that own all those different calibers and the 375...
When I target practice I shoot the remington core lockts..a box cost me about 44 bucks. On my hunting ammo I got it set up with 270gr. Recoil is not a problem as I have a brake...
Good luck with your choice...but for me, I love the 375.