I would say that to meet someone is that first contact when you actually meet them for the first time. So for example, if I met you in a bar, said hello but quickly left after only a very short conversation I would say we had met. Getting acquainted with someone is when you get to know them more after you meet. For example, we met in a bar but became more acquainted to one another by having a drink and spending some time getting to know more about each other. I would use the phrase, I want to meet people, it's much more informal and commonly used.

In that example, not much. Literally, meeting someone would be greeting each other, and getting acquainted would be getting to know one another.