환영합니다 vs 어서오세요
- 환영합니다: "Welcome (to a place, group, occasion, etc)!".
- 어서오세요: A greeting for someone arriving. Implies "Welcome", "Make yourself at home", "Good you're here", etc.
* There is also "잘 오셨어요" which is sort of in between the two in meaning.
For informal occasions like one's home or a small gathering, 어서오세요 and 잘 오셨어요 would work better.
In more public occasions or to emphasize "welcome", 환영합니다 and 잘 오셨습니다 are probably more appropriate.
Generally, 어서오세요 and 잘 오셨어요 sound nicer and warmer than 환영합니다.
In your examples, world, house, and group sound more personal, so all three would work fine.
For classroom and web page, I think 환영합니다 would work better.
These are not strict rules though, and I'm not sure which one might be better for "life".