To introduce Dharma, what categories of people are there? Buddha tailored his teachings to meet the particular needs of his audience. 
What are the different audiences then?

Here is a slightly related question: Should a beginner try to educate others about the benefits of Vipassana?
It is difficult to group the audience s into categories as the differences are many. Each person differs in each ones' level of understanding. The skillful and unskillful qualities of a persons mind differs from person to person. Then every questioners need is different from one to another. Some questions call for analytical answers, and others require categorical answers.
The Buddha had ten special powers. One of them was the ability to know positive and negative attribute of every being. So Buddha tailored the response depending on the person’s beliefs, or need, or level of knowledge.
The examples are many. One that came to mind was that of Cula Panthaka. The Buddha helped him to remove his ‘kleshas’ &amp; ‘upakkleshas’  and finally release his mind from all defilements. The story goes like this:

At the time of the Supreme Buddha, there were two brothers. They ordained in the Dispensation of the Buddha. The elder brother was very talented in remembering the Dhamma really well, but the second brother was unable to remember even one stanza. So, the elder brother asked his young brother to give up the monkhood and leave, “You can’t remember the Dhamma. You must go back home and start cultivating some plants.” But the younger brother didn’t want to leave the monkhood.
At the end, the younger-brother monk went to the temple’s gate and sat there crying. The Supreme Buddha came to him.
“Chūla Panthaka, why are you crying?”
“Oh dear Sir, my brother asked me to leave the temple.”
“Why was that?”
“I can’t remember any stanza I read. Therefore, he asked me to leave the monkhood and cultivate a field at home.”
“No, that’s not what you should do. Your brother doesn’t own this dispensation.”
The Supreme Buddha gently touched the monk’s head and took his hand, “Come with me.” The Supreme Buddha gave this young monk a small piece of cloth. “Dear monk, rub this cloth saying ‘cleaning, cleaning (rajō haranhan)’.” The young monk did as the Buddha told him. He saw that even though his intention was to clean the cloth, it was actually getting dirty gradually, “I rubbed this saying it to clean, but it is actually getting dirty.” His mind was well concentrated on to what happened to the cloth. The Supreme Buddha preached the Dhamma, so that the monk’s mind will be cultivated. In a moment, the young monk became an Arahant. See how his talent of realizing the Dhamma was concealed within him. If it was not the Buddha himself, who else would be able to do such a miracle? How many chances we may have missed and how many talents of us realizing life may have been concealed within us? Who would know how to unveil that talent in us?
It was this Chūla Panthaka Thero who became the first among the Bhikkhus who were able to create mental (Manōmaya) bodies. His brother monk didn’t know about it. He thought Chūla Panthaka Thero has gone home by that time. On that same day, all Bhikkhus went to alms-offering invitation. The Supreme Buddha told them that one monk is missing. Nobody knew about Chūla Panthaka Thero. The Supreme Buddha asked someone to go fetch the missing monk from the temple.
When he went to the temple, he saw one thousand monks. They were all alike. They were walking, cleaning the ground, and meditating. That person who came to fetch the monk ran back to the house and told the Supreme Buddha, “Dear Sir, there are thousand monks in the temple now.” The Supreme Buddha told him, “Please go back and ask what his name is. Touch the robe of the monk whoever answers first.” So, that person went back to the temple and said, “Who among you is called Chūla Panthaka Thero?” Then all thousand monks came forward saying, “I am… I am… I am…” As soon that person touched the monk who first answered, all other nine hundred ninety nine monks (bodies) disappeared.
He said, “Dear Sir, please come to lunch.” Chūla Panthaka Thero answered, “Dear devotee, you go please. I will come later.” The Supreme Buddha had the devotees at home to make a chair for Chūla Panthaka Thero. Then a Bhikkhu appeared from beneath the ground and sat on that chair; it was the Chūla Panthaka Thero.