It all started with Carlisle. He first turned Edward who was a patient of his and was dying of Spanish Influenza. After Edward, it was Esme, Carlisle's wife. After some time they thought Edward should have a partner, so, they turned Rosalie, who they found dying in the snow after being attacked by her drunken fiancee and his friends. The love affair between Edward and Rosalie never happened. Some years later, Rosalie came across Emmett who had been attacked by a bear in the woods. She asked Carlisle to change him for her. Alice and Jasper came in together. They are the only two that were not changed by Carlisle. Alice was a patient in a sanitarium. She had always had the gift of second sight and had foreseen falling in love with Jasper and finding the Cullen clan. Bella and Renesmee were the last to join the family. Bella was the first non-vampire to enter the family after marrying Edward. She did not become a vampire until after giving birth to Renesmee. Also, Bella was not bitten, Edward injected his venom into her after she gave birth to Renesmee.
Carlisle-changed by a vampire who is not named
Edward - changed by carlisle
Esme- changed by carlise
Rosalie- Changed by carlisle
Emmett-Changed by carlisle
Jasper and Alice came into the family at the same time but i dont know who was created first
Jasper- Changed by Maria(vampire from the south in 1861 you'll find out about her in Eclipse)
Alice- Changed by a vampire in the sanitarium she was in because of her visions
Bella- Changed by Edward
Carlisle: Carlisle was change around the 1600's. He can be seen as the head of the family since he-- with Esme-- brought the family together and presented a father and mother figure to them in a time of need.
Edward: Carlisle changed Edward since he was on the brink of dying from Influenza and as wish from his mother. He was the first one Carlisle has changed
Esme: Was changed by Carlisle as well after her attempt to commit suicide over a mountain after she had a miscarriage.
Rosalie: Rosalie was also changed by Carlisle after being beaten and abused then left on the streets to die.
Emmett: Although Rosalie saved Emmett from being mauled by a bear he was Changed by Carlisle.
Alice and Jasper came into the family at the same time, there's confusion on who was created first.
Bella- Then there's Bella who was changed by Edward after giving fatal birth to Renesmee.
emmett, rosalie, alice, jasper, edward
Carlise is the father and a couple of hundred year old. He changes Edward in 1918 because he is going to die of Influenza. He then changes Esme in 1921 after she tries to commit suicide because she is depressed over the loss of her baby. About 10 years later, Rosalie is changed by Carlise in hopes to be a match for Edward and she was beaten so badly, she was on the brink of death. Just a year or so later, Rosalie finds Emmett almost dead from a bear attack but brings him to Carlise to change him into a vampire. Alice and Jasper join the family in 1950 having been changed by other vampires.