A few of points to consider on the .375 H&H:
1. You can comfortably download them with Sierra 220 gr flat point bullets using SR 4759. These reduced loads, which are good deer hunting and plinking loads, are shown separately in the Sierra V ed. loading manual.
2. starting loads are frequently listed among the most accurate from the .375. Specifically, IMR 4064 and RL15 are two that I recall from the Nosler manual. I particularly like the Nosler 260gr AccuBond for non-dangerous game. This bullet and a moderate load feel to me like a 12g a. pump action shotgun and lighter than said shotgun shooting slugs.
3. shooting any heavy recoiling rifle such as the .444 Marin or the .375 H&H require good technique to handle the recoil and avoid developing a flinch. As an NRA Certified Rifle Instructor, I recommend all shooters, particularly those with limited experience, take a basic rifle course and develop good technique through the use of lighter recoiling calibers first.
4. I find a well-stocked bolt action rifle more comfortable to shoot than a traditional lever action rifle. I also find the Ruger No. 1 to be both accurate and manageable; it might be a goood alternative to a bolt action for some. (My No. 1 in 6.5x55 SE, loaded with 140gr Nosler A/Bs over VV N550, is one of my two favorite go-to rifle for most of my hunting. With a second round held between a couple of fingers on my left hand, I can get a follow-up shot pretty quickly if required).
Good luck and happy shooting,
FH