You can use the phrase "Nice to meet you" for all of those scenarios ! It is most commonly used in this scenario: When meeting someone for the FIRST time, at the end of the FIRST conversation. The second most common use is saying "Hi, it's nice to meet you", at the START of the FIRST conversation with a new person. This is more formal, and used with important people such as when meeting a new boss/employer, or as a polite greeting of someone personally important like a sibling's fiance. You do not have to say this at the end of the first conversation with a new acquaintance/friend, but it is considered polite to do so. You should NOT say this if you have met them before (because it will seem like you don't remember them). You SHOULD say this to important people when meeting them for the first time (for example, meeting a new boss/employer) even if you weren't happy to meet them. If you want to express that you were happy to meet someone for a second or third time, you would say "(it was) Nice seeing you (again)!", or "Nice talking again!", "Nice catching up!". Hope this helps. :)

You can use it when you are first introduced to someone. Then when you say goodbye, you can say it was really nice to meet you!