Meyer never gives an exact explanation for this variance from the traditional vampire other than the fact that she got the idea for the story from a dream. She dreamt of the meadow scene where two people were having an intense conversation about their doomed relationship. One was your average American girl (Bella), and the other was a boy who was "fantastically beautiful, sparkly, and a vampire" (Edward).
Meyers did not research traditional vampires when she began writing her book. Hers come from her imagination. As a matter of fact, there are very few similarities between her vampires and those like Nosferatu or vampire bats. Other than the fact that they are immortal, pale, and drink blood, her vampires are very different from "normal" vampires.
All of this is fiction. People have different ideas of vampires, some may say they feast off blood, others say they feast off emotions. In this case vampires cannot bear to be in the sunlight while in other cases they get burned. However, vampires can pull back together which is why they need to burn to avoid regeneration.
There is no specific reason as to why her vampires sparkle. The idea really came from her dream where she envisioned the scene with Edward and Bella in meadow and he was just there dazzling.
As for the reason her vampires need to be burned, in the Twilight novels the vampires are said to have the ability to pull themselves back together even if they are ripped in pieces. So to insure they do not regenerate they are burned until they are ashes. They was story in the Eclipse when Bella went with Jacob to a Quileute gathering and they were told the story of the birth of their ancestor as well as the first encounter with vampires. Where even hours of battle they could not defeat them because they kept regenerating so eventually decided to burn them and spread their ashes to make sure they never pulled themselves back together.
A good explanation would be that Stephenie Meyer is trying to lead the readers away from previous stereotypes of vampires. Around the time that we find this out in the book, we also find a number of other "myths" or "truths", according to Edward. Sticking to the preconceived notion that vampires are burned by sunlight would be too predictable and wouldn't really add anything to the storyline.
Check out Twlight (paperback edition), pg. 185. Edward and Bella discuss the various vampire myths.
In one of the books, it's written that vampires don't have fangs ... they have sharp teeth covered in venom. Stephenie just took some creative license when it came to her vampires!
It's not like there is an actual basis for the said characters. It's called fiction... a pigment of her imagination... and since its a love story, she wont want her readers to envision Edward as an ugly monster. She was so creative that people wanted to become Edward, a vampire.