Which one is the proper form of etiquette?

It would depend on the situation. What is going on in the room? Is it a party? I like to watch the door and greet people as they come into the party.

Either may be correct. The person entering should not interrupt and the group should welcome the person entering.

I believe its proper for a host to greet each invited guest but someone entering a room uninvited should wait until the appropriate time and then introduce themselves to the group

It is the role of the host to welcome the person first. If there is no host and the people don’t know each other, then it is up to whoever feels most outgoing to do the honors. It is appropriate for the person entering the room to catch an individual’s eye and greet them, and introduce themselves if no one in the group initiates introductions.

Depending on the situation, either behaviour might be appropriate. It the person entering is expected and perhaps the last to arrive, speaking immediately (if it will not interrupt an ongoing conversation) would be expected.

In other cases, waiting to be recognized and greeted would be more polite.

depends on what environment your entering.( office, party, meeting, church, on a date)...sometimes we fill like others should notice us and give us respectful hospitality. the truth is, life is busy so the office, party, even church where there is alot of activity some people misses seeing us and will not say anything or perhaps they do see us decides they will later on even if they forget to. Anyway, on a date when someone is expecting you. Well, I believe I should say hello first. Just to greet and show confidence in ourself. However, after greeting a person they should be gracious enough to respond friendly. If not, then seek to leave eary. their probably not worth your time anyway.

It may depend on what the situation is.

But normally, the person/people in the room would greet the person coming in.