I am assuming that you are asking for bullet recommendations for plains game, rather than dangerous game. If you are trying to come up with a one bullet solution for both, that changes the equation a bit. Like most of the "classic" safari chamberings, the .375 H&H doesn't generate enough velocity to need premium bullets. Heavy for caliber soft points will work just fine and have done so for a very long time. Load a 300 grain soft point to between 2550 and 2600 fps and go hunting. My personal favorite is the Sierra 300 grain Gameking. If you just have to have a premium bullet, go with a Partition or Accubond of the same weight.
Another very good option is the 250 grain Barnes TTSX. Load it to 2850 fps or so and take it hunting. My favorite powder for both the 300 grain Sierra and the 250 grain TTSX is RL-17.
If I were planning to take PG and DG on the same safari, I would load the Barnes 300 grain TSX to between 2550 and 2600 and use it for everything.