Oh, I think the First Doctor was clearly an alien. He contemplated going "back to (his) home planet" some time after the Dalek Masterplan stories.
A home planet in the distant future, though. Many alien planets in Doctor Who's future have been colonized by humans. That was the original implication, that the Doctor and Susan were far-future humans from a civilization that had mastered travel through space and time, and had developed intelligence and abilities that transcended 20th-century humanity.
In "The Sensorites," the Doctor said that cats "can see better than we humans" at night. Later, a Sensorite referred to him as a human being, though the Doctor wasn't there to confirm or refute it. Similarly, in "The Chase," the Daleks referred to the TARDIS crew as "the four humans," and Brett in "The War Machines" described the Doctor as having a "special human brain." Captain Blade in "The Faceless Ones" called the Doctor human, and the Doctor didn't correct him. The Daleks in "The Evil of the Daleks" referred to the Doctor as "more than human," but attributed it to him being a time traveler. Overall, the writers seemed to assume that the Doctor was human. It wasn't until "The War Games" that he was clearly established as being from an alien race, and not until "Spearhead from Space" that he was established as having two hearts.