The 375 H&H Magnum, 416 Rigby and 458 Lott are all adequate to take dangerous game animals including elephant and buffalo. For stopping power for a charging animal, I would say that the 458 Lott is the best. Comparing the 375 H&H Magnum and the 416 Rigby is a bit more difficult; in my opinion they're about equal.
As for bullet size to use, you would go for the heaviest bullet available for the cartridge when hunting dangerous game. In the 375 H&H Magnum, the most commonly available heaviest bullet weight would be 300 grains. For the 458 Lott, the most common heavy bullet weight would be 500 grains though weights up to 600 grains are available; I think 500 grains is enough. Since I don't load for a 416 Rigby, I don't remember bullet weights for it.
As far as bullet types to use, traditionally solids were used for dangerous game. That has changed somewhat since the advent of certain tough premium bullets like Barnes. Now, many professional hunters recommend a premium bullet for things like buffalo perhaps with solids for follow-up shots. Solids are still recommended for elephant hunting.
At least in "los Estado Unidos" Hornady bullets are the most economical bullets to buy for shooting at targets. The Hornady full metal jacket bullets are quite accurate in my 375 H&H Magnum and 458 Lott.
And there are several principles you have to learn in order to deal with women:
1. Women can't count past 3. This means you need at least 3 guns. After you get 3 guns, you wife will refer to them as "estos rifles" and you can get as many as you like. My wife recently opined that I probably had a least a dozen gun barrels (I have Thompson/Center products with interchangeable barrels)...if she only knew.
2. Learn the dump truck principle. Say you want a pickup truck. Don't tell your wife you want a pickup truck; tell her you want a dump truck and then compromise and say you'll accept a pickup. To make this work with your wife, tell her you want a 50 BMG and show her pictures of it; then compromise and tell her you'll get a 458 Lott instead.
I have many more recommendations on how to deal with wives too extensive to go into now since I have to take the garbage out and get dressed.