When you say, people or person, it sounds like you're emphasizing that they're human beings. Which is unnecessary in some cases. Coming from an American background, I'd simplify things and say 1. "This is Peter, this is Paul and this is Mary." 2. Peter, Paul and Mary (they) are my classmates.

If you are introducing them to someone it would be better to say " Let me introduce you .This is Peter,this is Paul and this is Mary.They are my classmates."

Saying "This person is Peter, Paul, and Mary." would not be correct, since "person" refers to a single individual, but you list multiple names. Saying "This person is ..., this person is ..." is technically correct, but sounds strange because it is very verbose. You would only use this/that for every person if, for example, you are pointing out people in a crowd. "This is Peter, that is Paul, and that is Mary." would only be used if you are physically pointing at the people as you say their names. "These people are my classmates ..." is grammatically correct, but a native would rarely speak this way. It is best to leave "people" out and use just "These are my classmates ..." The only situation where I would phrase the sentence this way is so: A: "Man, these people are terrible." B: "These people are my friends!" Speaker B says this because he is offended by speaker A. B's use of the complete phrase "these people" is intended to put extra emphasis on the group that was mentioned in order to 1) make it clear that B has a connection to the group, and 2) show that, because of B's connection to the group, B disagrees with A's assessment and is offended. Note, however, that B would not subsequently list their names here, since introducing his friends is no longer the objective of the sentence.