Ian Mortimer believes, not that Edward III was actually a "perfect king," but that he was striving towards it - that it was one of his goals in life to live up to the great prophecies made at his birth in 1312.
Edward III was the grandson of Edward I, "Hammer of the Scots," and the son of Edward II, a weak king, and Isabella of France, daughter of Philip IV "the Fair." (The latter epithet relates to Philip's hair color, not his personality; he was a tough king, and sometimes a very cruel one.) Isabella would be the only one of Philip's four children (he also had three sons) to produce male children who would live to adulthood, which would result in great tragedy for France for the next hundred years.
Few English kings can have come to the throne in a more perilous situation - he was a boy of fourteen, and the puppet of his mother and particularly of her lover, the ambitious Roger Mortimer, Earl of March. For diplomatic reasons he was almost immediately married to the twelve-year-old Phillipa of Hainault (a principality in what is now Belgium). He had few friends, and little time not monitored by either Isabella or Mortimer. He was told, and spread the news far and wide, that his father, Edward II, died of grief in September of that year, while in confinement at Berkeley Castle.
At seventeen, in 1330, already a father, and aware of how precarious his situation was, he took an enormous chance, and personally overthrew Mortimer in the middle of the night, while they were staying at Nottingham Castle. He would rule alone for the rest of his life, which would be long (he died only in 1376).
However, Mortimer argues, Edward III already knew that he had been lied to in 1327, and that his father still lived. It's a really interesting argument, and I think he has pretty good evidence. (Mortimer has a fairly long article on his webpage laying out the general lines of his argument: http://www.ianmortimer.com/EdwardII/death.htm .)
Edward III's future prowess as a warrior king is legendary - he would lead the English to victories over the Scots, at Halidon Hill, and the French, at Crecy, Poitiers, and Sluys (the great naval battle of the Hundred Years' War). What may be less famous is his attention to, and building up of, the English Parliament, his great building projects (he had hot and cold running water in his bathroom!), or his fascination with the new inventions and machinery, such as clocks. (There's also an interesting bit about Edward III as a model for Arthur in medieval romances.)
It may have taken me a year to finish, but I kept getting distracted. I blame you lot, as I keep thinking "well, that book looks interesting..."