Why the doctor? He's the last of the timelords, an omnipotent, omniscient creature who seems to never die, when on death's doorstep he regenerates into the same organism but with a changed personality, set of tastes, interests, and most obviously body. He typifies the stereotype of an eccentric English genius, in his tardis (which in the distant past was a polymorphic time machine, which would fit in with the surroundings until it broke and remained forever a police box), which is bigger on the inside than on the outside, and travels with a host of assistents who don't really understand him.
The doctor uses intellect rather than physical power, he shuns guns and weaponry, knowing every problem has a solution which can be resolved by wit. Many a time the viewer doesn't understand his motives, though discovers the admirable reason in a future episode.
He is like Merlin, like Dumbledore, I wouldn't be surprised if J.K.Rowling, a fan of doctor who herself used the figure of the doctor as an inspiration for Dumbledore. By fooling his enemies and acquintances that he hasn't a clue, with humor (the 2nd and 4th Doctors bought fame to the simple question 'anyone want a jellybaby' in the most periculous moments).
Perhaps most significantly, his character and his species is somewhat a mystery, and as one continues to watch and read the stories, one gets a sense that this a very powerful ancient being.
Ultimate mix, titles and regenerations from 1960s til now.
Regenerations, a little more detail
10th and 11th doctor-s themes