RedShirtNo5.1
Explorer
You could go for in-jokes, like having Scott Baluka, Michael J. Fox and Keanu Reeves show up.That way, you get to see a bunch of likely & unlikely sorts- Bill Bailey, Kenneth Brannagh, Helen Mirren, Brian May, Ardal O'Hanlon, Idris Elba- in the role if only for a few minutes of screen time until his regeneration stabilizes.
To me the most important feature is that the Doctor is British. Age, skin color and social class don't seem important.
I think even a female Doctor could work. There are handwaves as to why it didn't happen.
-The ability to change gender on regeneration depends on a gene in the Timelord population, which the Doctor did not have. However, due to applied phlebotinum the Doctor just got that gene.
-An unexpected regeneration tends to default to small changes in body type, whereas a deliberate regeneration isn't so limited.
-"I could have regenerated as female before, but I was worried that it would have bothered my previous companions."