Assuming you aren't going to give the rifle away as a tip to the PH...
Get a good fairly wide-range variable. The .375 is so versatile, it can be used under nearly all conditions, lighting, weather, and on nearly all animals, certainly all North American animals.
I put a Leupold 4x on my .375 back in c.1988 and frankly, wish I'd have put a 3x9 variable on it. I find many times in the field when a bit more power is helpful; final judging of the head and "threading the needle" thru brush being the two main ones.
A 3x9 in strong QD mounts that return the scope to zero is the best setup for a .375 H&H I can imagine.
Just my $.02 {now worth about $.015 due to the weak dollar... }
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