Mother Teresa from her earliest years felt drawn to the religious life, especially that of a missionary. At the age of 18 she joined the Sisters of Loreto and, after several years of training in India, made her vows as a sister. She was not a nun. Nuns pretty much spend there entire life behind the doors of a monastery and do not work in the outside world..
In her "biography", I believe she had a dream. She had gotten a
calling from God. I also remember reading that she had always
wanted to serve God, and help people.
People don't normally "choose" to become a sister, a nun, or a priest. They can choose NOT to become a religious, but it is God who chooses a person, it is called a "call", the Latin word is Vocation: it is a call from God. The person chooses to accept the call. Mother Teresa was very adamant about receiving her call from God - she writes about it extensively in her autobiography.
Mother Teresa did not become a nun, she became a sister. In the Catholic Church, a nun is a woman who takes solemn vows in a monastery and remains there for life. Sisters do not live in a monastery, but out in the world, they teach, nurse, etc. Sisters take simple vows, or perpetual promises which are renewed yearly. This arose in the 18th and 19th centuries, before that time, all women religious were required by the Vatican to be in enclosed monasteries. It was only in the past few centuries that nursing Orders, teaching Orders, etc. arose. Nevertheless, the call comes from God, you only choose to obey or ignore it, Mother chose to accept it, as she accepted God's will for her throughout her life.