As others have said, scope it like you would any "standard" hunting rifle. I've got a VX-III 1.75-6x32mm on mine, and that's as low as I would recommend going. The low light performance of that scope is reasonable IMHO -- it's served me well in the last 15 minutes of legal shooting light when the pressure was on to clean up a mess that started when a Cape Buff decided not to play nice and surrender at the first shot. That said, though, something like a 3.5-10x40mm will have a noticeably better twilight factor, which is nice to have, but seldom essential.
The thing with the .375 is that it's really a medium bore jack-of-all-trades, not a heavy "stopping" rifle. With a trajectory that very closely mirrors a .30-06, it should be outfitted with glass that allows for quick shooting up close on big scary stuff as well as for taking a 300+ yard shot on a deer-sized critter.
If I were to scope my .375 again, I'd likely go with something more along the lines of a 2.5-8x.