My 2 cents.
.375 isn't the worst by far, but it still kicks. Even if the rifle is well made and balanced and absorbs recoil, the scope will feel it. Lots of cheaper scopes are intended for North American type rifles, which doesn't usually extend to .375.
Brand is up to you, but rather buy second hand and buy quality than buy something that won't last or won't give you the performance you need in a dangerous game rifle. Leupold is very good, as are the European names, but they are much more expensive. Having said that, even a new Swarovski Z3 in 3-10x42 is $800, and some will go lower (just bought one in Canada for quite a bit less).
Apart from that, in my view you need:
1. Not too much power. The .375 to reasonable even at longer ranges, but most people don't buy it for that, so you don't need to get a huge scope with 18x or whatever. I think the 3-10x is about all anyone should need. You could even go lower than 3x, but to keep the upper end means more expense.
2. Get detachable mounts. It's always easier to follow up on wounded dangerous game without a scope. If you want to be helpful, you should be able to take the scope off. That means practice with iron sights.
3. They are more expensive, but if you can find a good one used, an illuminated reticle is a wonderful option to have as light fades (not everyone here agrees with me on this . . .).
Good luck with the purchase, and enjoy it. This is half the fun of hunting!