There have been Christian virgins since the earliest times. For example, St. Mary the Virgin lead a house of virgins until her Dormition. But monasticism as we know it today was started by St. Antony, who was a Copt (Egyptian). He started living celebatly at the outskirts of the city like the other celebates, but it wasn't enough for him. He moved progressively further out into the desert in search of solitude. He thought to himself that he was the first on to do this, and so God told him to walk 3 days into the desert, where he found St. Paul the Anchorite, who had been living without seeing another human being for 8 decades. St. Paul is the first anchorite, and St. Antony is the first monk, since he was the first one to be a father of children in a rudimentary monastary. St. Athanasius the Apostolic was a friend of St. Antony, and wrote the book "The Live of St. Antony" which he propogaed while he was in exile at the Church of Rome. Through this book a love for monasticism spread rapidly throughout the Church. People flocked to the deserts of Egypt to learn about this way of live, and then take it back to their homelands. St. Jerome was one notable Western Father who visited the monastaries in the Egyptian desert.
The life of Antony is available in most bookstores, or from amazon.com. It's a very easy to read and fun book, telling the story of an amazing saint, written by an amazing saint.
The lives of St. Antony and St. Paul can be read from the Coptic Synexarium (the Chronical of the Saints) at
http://saintmark.com/topics/synexarion/antony.html and at
http://saintmark.com/topics/synexarion/stpaulus-hermit.html
All our bishops and the Pope are selected only from the monks, and continue to be monks. H.H. Pope Shenouda travels all over the world, consecrating every church, visiting all the churches, and he ordains all the priests in Egypt, he has also written over 100 books, and yet he spends 1/2 of every week in his monastary. Every bishop's residence is at a monastary, and in addition to his diocese, the bishop is usually the abbot of the monastary.